28:["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"Let the equation of tangent to parabola"}}] 35:T53c,y² = 16x is y = mx +

{4 \over m}

...... (1)29:["$","li","1",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":2}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$35"}}]]}] 2a:["$","li","2",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":3}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"It is given that tangent to xy = -4 .........(2)"}}]]}] 2b:["$","li","3",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":4}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"Solving (1) and (2) we get"}}]]}] 36:Ta0f,

x\left( {mx + {4 \over m}} \right) + 4 = 0

2c:["$","li","4",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":5}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$36"}}]]}] 37:Tb65,

\Rightarrow m{x^2} + {4 \over m}x + 4 = 0

2d:["$","li","5",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":6}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$37"}}]]}] 38:Ta16,Now for tangent D = 0

\Rightarrow {{16} \over {{m^2}}} - 16m = 0

2e:["$","li","6",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":7}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$38"}}]]}] 39:T712,

\Rightarrow {m^3} = 1

\Rightarrow

m = 12f:["$","li","7",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":8}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"$39"}}]]}] 30:["$","li","8",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":9}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"Now putting value of m in Equation (1)"}}]]}] 31:["$","li","9",{"className":"flex items-start gap-3","children":[["$","span",null,{"className":"mt-0.5 flex h-5 w-5 shrink-0 items-center justify-center rounded-md bg-surface-sunken font-mono text-[11px] text-ink-400","children":10}],["$","div",null,{"className":"min-w-0 max-w-[68ch] flex-1 text-[15px] leading-relaxed text-ink-600 [&_.katex-display]:my-3 [&_.katex-display]:overflow-x-auto","dangerouslySetInnerHTML":{"__html":"y = x + 4 or x – y + 4 = 0"}}]]}] 32:["$","footer",null,{"className":"flex flex-wrap gap-2 border-t border-rule pt-4 text-[13px] text-ink-400","children":["JEE Main 2019 · 12 Apr, Evening shift · Q4684",["$","span",null,{"className":"text-rule-strong","children":"·"}],"Parabola"]}] 33:["$","section",null,{"className":"flex flex-col gap-3 border-t border-rule pt-6","children":[["$","h2",null,{"className":"m-0 text-[12px] font-semibold uppercase tracking-[0.06em] text-ink-400","children":["More on ","Parabola"]}],["$","ul",null,{"className":"m-0 flex list-none flex-col gap-2 p-0","children":[["$","li","f408440a-3f31-4d94-bfab-f4e284db3e73",{"children":["$","$L8",null,{"href":"/q/if-the-length-of-the-latus-rectum-of-a-parabola-1l6kkcjlr","className":"flex flex-col gap-0.5 rounded-xl bg-surface-card px-4 py-3 no-underline shadow-soft transition-shadow hover:shadow-lift","children":[["$","span",null,{"className":"text-[15px] font-bold text-ink-900","children":"Parabola"}],["$","span",null,{"className":"text-[13px] text-ink-400","children":"JEE Main 2022 · 27 Jul, Evening shift · Q4752"}]]}]}],["$","li","9132ba70-b880-4507-adeb-8a92397881d9",{"children":["$","$L8",null,{"href":"/q/if-the-tangents-drawn-at-the-points-mathrm-p-1l6m5skm4","className":"flex flex-col gap-0.5 rounded-xl bg-surface-card px-4 py-3 no-underline shadow-soft transition-shadow hover:shadow-lift","children":[["$","span",null,{"className":"text-[15px] font-bold text-ink-900","children":"Parabola"}],["$","span",null,{"className":"text-[13px] text-ink-400","children":"JEE Main 2022 · 28 Jul, Morning shift · Q4753"}]]}]}],["$","li","ea513726-55c1-4524-bf3e-a577009434f1",{"children":["$","$L8",null,{"href":"/q/let-be-a-point-on-the-parabola-y-1l6jbzo79","className":"flex flex-col gap-0.5 rounded-xl bg-surface-card px-4 py-3 no-underline shadow-soft transition-shadow hover:shadow-lift","children":[["$","span",null,{"className":"text-[15px] font-bold text-ink-900","children":"Parabola"}],["$","span",null,{"className":"text-[13px] text-ink-400","children":"JEE Main 2022 · 27 Jul, Morning shift · Q4751"}]]}]}],["$","li","34c57ca6-1bd2-4c70-b9c1-628c03aaf2f6",{"children":["$","$L8",null,{"href":"/q/tangents-drawn-from-the-point-8-0-to-the-hrCdUD5PJzdt0puJ8q5I7","className":"flex flex-col gap-0.5 rounded-xl bg-surface-card px-4 py-3 no-underline shadow-soft transition-shadow hover:shadow-lift","children":[["$","span",null,{"className":"text-[15px] font-bold text-ink-900","children":"Parabola"}],["$","span",null,{"className":"text-[13px] text-ink-400","children":"JEE Main 2018 · 15 Apr, Evening shift · Q4667"}]]}]}]]}]]}]

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