JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let the function \(f(x)=2 x^{2}-\log _{e} x, x>0\), be decreasing in \((0, a)\) and increasing in \((a, 4)\). A tangent to the parabola \(y ^{2}=4 ax\) at a point \(P\) on it passes through the point \((8 a, 8 a-1)\) but does not pass through the point \(\left(-\frac{1}{a}, 0\right)\). If the equation of the normal at \(P\) is \(\frac{ x }{\alpha}+\frac{ y }{\beta}=1\), then \(\alpha+\beta\) is equal to-
- A \(45\)
- B \(44\)
- C \(43\)
- D \(44\)
Answer & Solution
Correct Answer
(A) \(45\)
Step-by-step Solution
Detailed explanation
Let \(P \left( x _{1}, y _{1}\right)\) be any point on \(y ^{2}=4 ax\) \(\frac{1}{ y _{1}}=\frac{3- y _{1}}{4- x _{1}} \Rightarrow y _{1}^{2}-6 y _{1}+8=0 \) \(y _{1}=2,4\) \(P (8,4) \text { as } P (2,2) \text { rejected }\) \(\text { Equation of normal at } P\)…
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