Question

Equation of a common tangent to the circle, x2 + y2 = 50 and the parabola, y2 = 40x can be.

Answer 1

Step-by-step explanation:

What's your doubt?

Maths

Bookmark

The equation of common tangent to the circle x

2

+y

2

=2 and parabola y

2

=8x is

share

Share

Answer

Correct option is

B

y=x+2

Given, y

2

=8x

∴4a=8⇒a=2

Any tangent of parabola is,

y=mx+

m

a

⇒mx−y+

m

2

=0

If it is a tangent to the circle x

2

+y

2

=2, then perpendicular from centre (0,0) is equal to radius

2

.

∴

m

2

+1

m

2

=

2

⇒

m

2

4

=2(m

2

+1)

⇒m

4

+m

2

−2=0

⇒(m

2

+2)(m

2

−1)=0

⇒m=±1

Hence, the common tangents are y=±(x+2).