The parabola x=y2+a y+b intersect the parabola x2=y at (1,1) at right angle. Which of the following is/are correct?

Question

The parabola x=y2+a y+b intersect the parabola x2=y at (1,1) at right angle. Which of the following is/are correct? (A) a=4, b=-4 (B) a=2, b=-2 (C) Equation of the director circle for the parabola x=y2+a y+b is 4 x+1=0. (D) Area enclosed by the parabola x=y2+a y+b and its latus rectum is (1/6).

Tardigrade Admin · Accepted Answer

Correct answer is (c) Equation of the director circle for the parabola x=y2+a y+b is 4 x+1=0.Correct answer is (d) Area enclosed by the parabola x=y2+a y+b and its latus rectum is (1/6).

Q. The parabola $x = y^{2} + a y + b$ intersect the parabola $x^{2} = y$ at $(1, 1)$ at right angle. Which of the following is/are correct?

$a = 4, b = - 4$

$a = 2, b = - 2$

Equation of the director circle for the parabola $x = y^{2} + a y + b$ is $4 x + 1 = 0$ .

Area enclosed by the parabola $x = y^{2} + a y + b$ and its latus rectum is $\frac{1}{6}$ .

Correct answer is (c) Equation of the director circle for the parabola $x = y^{2} + a y + b$ is $4 x + 1 = 0$ . Correct answer is (d) Area enclosed by the parabola $x = y^{2} + a y + b$ and its latus rectum is $\frac{1}{6}$ .

Q. The parabola x=y2+ay+b intersect the parabola x2=y at (1,1) at right angle. Which of the following is/are correct?

a=4,b=−4

a=2,b=−2

Equation of the director circle for the parabola x=y2+ay+b is 4x+1=0.

Area enclosed by the parabola x=y2+ay+b and its latus rectum is 61​.