1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The angle between the tangent at any point P and the line joining P to the origin, where P is a point on the curve ln(x2+y2)=ctanâˆ’1yx,c is constant, is

A
Independent of x
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
Independent of y
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Independent of x but dependent on y
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
Independent of y but dependent on x
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is B Independent of y Let P(x,y) be a point on the curve ln(x2+y2)=ctan−1yx. Differentiating both sides with respect to x, we get 2x+2yy′(x2+y2)=c(xy′−y)(x2+y2) ⇒y′=2x+cycx−2y=m1 (say) Slope of OP=yx=m2 (say) (where O is origin) Let the angle between the tangents at P and OP be θ. Then, tanθ=∣∣∣m1−m21+m1m2∣∣∣ =∣∣ ∣ ∣ ∣∣2x+cycx−2y−yx1+2xy+cy2cx2−2xy∣∣ ∣ ∣ ∣∣ =∣∣∣2c∣∣∣ ⇒θ=tan−1(2c) which is independent of x and y.

Suggest Corrections
7
Join BYJU'S Learning Program
Join BYJU'S Learning Program