Question

The tangent at origin to the curve
y^2 = 4ax - x^2 makes an angle of 90° to X-axis. The value of a is​

Answer 1

Step-by-step explanation:

Any line through origin is y=mx. Since, it is a tangent to y

2

=4a(x−a), it will cut it in two coincident points.

So, roots of m

2

x

2

−4ax+4a

2

=0 are equal.

Product of slope =−1 i.e., b

2

−4ac=0

⇒16a

2

−16a

2

m

2

=0

⇒m

2

=1 or m=1,−1

Hence, required angle is right angle i.e.,

2

π