Question

An equation of a common tangent to the parabola y^2=4x and x^2=4y is

Answer 1

Answer:

−1

Step-by-step explanation:

y2=4x has a tangent y=mx+1m

Which is also tangent to x2=4y so this tangent passes through x2=4y

⇒x2=4(mx+1m)

x2−4mx−4m=0

Roots of this equation is same as their is one tangent hence

B2=4AC

(−4m)2=4×1×−4m

16m2=−−16m

m3=−1

Hence m=−1

Equation of tangent y=−x−1

x+y=−1