Question

A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with

• A. Length of latus rectum 3
• B. Length of latus rectum 6
• C. $Focus \bigg(\frac{4}{3},0\bigg)$
• D. $Focus \bigg(0,\frac{3}{4}\bigg)$

Answer 1

Answer: (A)

Length of latus rectum 3

Answer 2

$2x-y \frac{dx}{dy} = 0$

tangent at $P:y-y =\frac{dy}{dx}(y-x)$

$∴ 2 \frac{dy}{y} = \frac{dx}{x}$

$⇒ 2Iny = Inx+Inc$

$⇒ y^2 = cx$

At coordinates $(3, 3)$ curves pass through
Hence, $c = 3$

Therefore, the is parabola :

$y^2 = 3x$

So Length of latus rectum is $3$.

Hence, the correct option is (A): Length of latus rectum is $3$