JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(S\) be the set of all \(a \in N\) such that the area of the triangle formed by the tangent at the point \(P ( b , c ), b , c \in N\), on the parabola \(y ^2=2 ax\) and the lines \(x=b, y=0\) is \(16\) unit \(^2\), then \(\sum_{\text {aes }} a\) is equal to \(..........\).
- A \(145\)
- B \(144\)
- C \(143\)
- D \(146\)
Answer & Solution
Correct Answer
(D) \(146\)
Step-by-step Solution
Detailed explanation
As \(P ( b , c )\) lies on parabola so \(c ^2=2 ab\) Now equation of tangent to parabola \(y ^2=2 ax\) in point \(\text { form is } y_1=2 a \frac{\left(x+x_1\right)}{2},\left(x_1, y_1\right)=(b, c)\) \(\Rightarrow y c=a(x+b)\) For point \(B\), put \(y =0\), now \(x =- b\) So,…
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