The correct option is
A True
Equation of tangent to parabola y2=4ax at point (x1,y1) is given by yy1=2a(x+x1)→ ---(1)Also (x1,y1) lies on parabola
⇒y21=4ax1→ (2)
Equation of given circle is
$x^2+y^2=r^2.$
Let (h,k) be the mid point of PQ
∵ equation of chord whose mid point is (h,k) is given by T=x1 i.e xh+yk=h2+k2→ (3)
equation equation (1) and (3) are identical.
Therefore 2ah=−y1k=2ax−(h2+k2)
⇒y1=−2akh→ (4)
and x1=−(h2+k2)h→ (5)
putting the value of x1 and y1 from equation (4) and (5) is (2).
we get, (−2akh)2=4a(−(h2+k2)h)
⇒4a2k2h2=−4ah(h2+k2)
4ah(h2+k2)+4a2k2=0
⇒ah(h2+k2)+a2k2=0
⇒ Locus of mid-point of PQ is given by x(x2+y2)+ay2=0
∴ This statement is True.
![2117459_1131484_ans_6734be02d433461686ea126dc4fe0346.png](https://search-static.byjusweb.com/question-images/toppr_invalid/questions/2117459_1131484_ans_6734be02d433461686ea126dc4fe0346.png)