JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If one end of a focal chord of the parabola, \(y^2 = 16x\) is at \((1, 4),\) then the length of this focal chord is
- A \(25\)
- B \(24\)
- C \(22\)
- D \(20\)
Answer & Solution
Correct Answer
(A) \(25\)
Step-by-step Solution
Detailed explanation
\({y^2} = 4ax = 16x \Rightarrow a = 4\) \(A\left( {1,4} \right) \Rightarrow 2.4{t_1} = 4 \Rightarrow {t_1} = \frac{1}{2}\) \(\therefore \) length of focal chord \( = a{\left( {t + \frac{1}{t}} \right)^2}\) \( = 4{\left( {\frac{1}{2} + 2} \right)^2} = 4.\frac{{25}}{4} = 25\)
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