Parabola y 2 = 4 a ( x - c 1 ) & x 2 = 4 a ( y - c 2 ) touch each other where c 1 & c 2 are variables, then locus of their point of contact is:

Question

Parabola $y^{2} = 4 a (x - c_{1})$ & $x^{2} = 4 a (y - c_{2})$ touch each other where $c_{1}$ & $c_{2}$ are variables, then locus of their point of contact is:

Smart Achievers · Accepted Answer

(3)

$Let p (h, k) be the point of contact$

$2 y \frac{d y}{d x} = 4 a & 2 x = 4 a \frac{d y}{d x}$

$Both \frac{d y}{d x} are same$

$\Rightarrow \frac{4 a}{2 y} = \frac{2 x}{4 a}$

$\Rightarrow x y = 4 a^{2}$

Solution

Q.
Parabola $y^{2} = 4 a (x - c_{1})$ & $x^{2} = 4 a (y - c_{2})$ touch each other where $c_{1}$ & $c_{2}$ are variables, then locus of their point of contact is:

1 $x y = a^{2}$

2 $x y = 2 a^{2}$

3 $x y = 4 a^{2}$

4 $x y = 3 a^{2}$

Ans.
(3)

$Let p (h, k) be the point of contact$

$2 y \frac{d y}{d x} = 4 a & 2 x = 4 a \frac{d y}{d x}$

$Both \frac{d y}{d x} are same$

$\Rightarrow \frac{4 a}{2 y} = \frac{2 x}{4 a}$

$\Rightarrow x y = 4 a^{2}$

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Solution

Q. Parabola y2=4a(x-c1) & x2=4a(y-c2) touch each other where c1 & c2 are variables, then locus of their point of contact is:

1 xy=a2

2 xy=2a2

3 xy=4a2

4 xy=3a2

Ans. (3) Let p(h,k) be the point of contact 2ydydx=4a & 2x=4adydx Both dydx are same ⇒4a2y=2x4a ⇒xy=4a2