The locus of the centre of a circle which cuts orthogonally the parabola y2=4 x at (1,2) will pass through

Question

The locus of the centre of a circle which cuts orthogonally the parabola y2=4 x at (1,2) will pass through (A) (3,4) (B) (4,3) (C) (5,3) (D) (2,4)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/f27eb5fd9fcb0d3b0237fd2c37d29803-.png" /> Tangent to the parabola y2=4 x at (1,2) will be the locus, i.e., 2 y=2(x+1) or y=x+1

Q. The locus of the centre of a circle which cuts orthogonally the parabola $y^{2} = 4 x$ at $(1, 2)$ will pass through

$(3, 4)$

$(4, 3)$

$(5, 3)$

$(2, 4)$

Tangent to the parabola $y^{2} = 4 x$ at $(1, 2)$ will be the locus, i.e.,
$2 y = 2 (x + 1)$
or $y = x + 1$

Q. The locus of the centre of a circle which cuts orthogonally the parabola y2=4x at (1,2) will pass through

(3,4)

(4,3)

(5,3)

(2,4)