MHTCET 2016 Math Solved Paper

(b) Let centre of circle on X-axis be (K, 0).
∴ the radius of circle will be K.

∴ the equation of circle having centre (K, 0) and radius K is
(x−K)2+(y−0)2=K2
⇒ x2+K2 - 2hx + y2=K2
⇒ x2−2Kx+y2 =0 ...(i)
On differentiating both sides w.r.t x, we get
2x−2K+2y

dy

dx

=0
⇒ K=x+y

dy

dx

......(ii)
From equations (i) &( ii) we get
x2−2(x+y

dy

dx

)x + y2=0
⇒ −x2+y2 - 2xy

dy

dx

=0
⇒ (x2−y2) + 2xy

dy

dx

=0