CUET · MATHS · PYQ PAPER 2023
The points on the curve \(2 x=y^2\) which are nearest to the point \((5,0)\) lie in
A. I Quadrant
B. II Quadrant
C. III Quadrant
D. IV Quadrant
Choose the correct answer from the options given below:
- A A, B only
- B B, C only
- C C, D only
- D A, D only
Answer & Solution
Correct Answer
(D) A, D only
Step-by-step Solution
Detailed explanation
\(D^2 = (x-5)^2 + y^2\) \(x = \frac{y^2}{2}\) \(D^2(y) = \left(\frac{y^2}{2}-5\right)^2 + y^2\) \(\frac{d(D^2)}{dy} = 2\left(\frac{y^2}{2}-5\right)(y) + 2y = y(y^2-10)+2y = y^3-8y\) \(y^3-8y = 0 \Rightarrow y(y^2-8)=0 \Rightarrow y=0, y=\pm\sqrt{8} = \pm 2\sqrt{2}\) If \(y=0\),…
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