Parabola $y^2=4a(x-c_1)$ and $x^2=4a(y-c_2)$ touch each other where $c_1,c_2$ are variables. Then locus of their point of contact is
Step-by-Step Solution
Key Concept: At point of tangency, slopes of tangents are equal and contact point lies on both curves
Let contact point $(h,k)$. Tangent to $y^2=4a(x-c_1)$: $ky=2a(x+h-2c_1)$. Tangent to $x^2=4a(y-c_2)$: $hx=2a(y+k-2c_2)$. Matching slopes: $hk=2a^2... $\Rightarrow xy=2a^2$.
Correct Answer: 2