A variable circle passes through the fixed po | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the centre of the circle be $(h, k)$.Since the circle touches the $y$-axis,the radius of the circle is equal to the absolute value of the $x$-

Vedclass · Accepted Answer

$A$ parabola

Vedclass · Answer

(D) Let the centre of the circle be $(h, k)$.Since the circle touches the $y$-axis,the radius of the circle is equal to the absolute value of the $x$-coordinate of the centre,i.e.,$r = |h|$.Since the circle passes through the point $(2, 0)$,the distance from the centre $(h, k)$ to $(2, 0)$ must equal the radius $r$.Thus,$(h - 2)^2 + (k - 0)^2 = h^2$.Expanding this,we get $h^2 - 4h + 4 + k^2 = h^2$.Simplifying,we get $k^2 = 4h - 4$.Replacing $(h, k)$ with $(x, y)$,the locus of the centre is $y^2 = 4x - 4$,which represents a parabola.

$A$ variable circle passes through the fixed point $(2,0)$ and touches the $y$-axis. Then the locus of its centre is

Similar Questions

The equation of the locus of the midpoints of the chords of the circle $4x^2 + 4y^2 - 12x + 4y + 1 = 0$ that subtend an angle of $\frac{2\pi}{3}$ at its center is

The equation of the locus of a point which moves so as to be at equal distances from the point $(a, 0)$ and the $y$-axis is

If a circle passes through the point $(1, 2)$ and cuts the circle $x^2 + y^2 = 4$ orthogonally,then the equation of the locus of its centre is

The two points $A$ and $B$ in a plane are such that for all points $P$ lying on a circle satisfying $\frac{PA}{PB} = k$,then $k$ will not be equal to:

The locus of the midpoint of a chord of the circle $x^{2} + y^{2} = 4$ which subtends an angle of $45^{\circ}$ at the major arc of the circle is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module