If the angle between a pair of tangents drawn | vedclass

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

Question

(D) The given circle is $x^2+y^2-4x+2y+3=0$. Comparing with $x^2+y^2+2gx+2fy+c=0$,we get $g=-2, f=1, c=3$. The center is $(2, -1)$ and the radius $r =

Vedclass · Accepted Answer

$x^2+y^2-4x+2y+1=0$

Vedclass · Answer

(D) The given circle is $x^2+y^2-4x+2y+3=0$. Comparing with $x^2+y^2+2gx+2fy+c=0$,we get $g=-2, f=1, c=3$. The center is $(2, -1)$ and the radius $r = \sqrt{g^2+f^2-c} = \sqrt{4+1-3} = \sqrt{2}$. If the angle between the tangents is $\frac{\pi}{2}$,the locus of the point $P$ is the director circle. The equation of the director circle is $(x-h)^2+(y-k)^2 = 2r^2$,where $(h, k)$ is the center. Substituting the values: $(x-2)^2+(y+1)^2 = 2(\sqrt{2})^2 = 4$. Expanding this: $x^2-4x+4+y^2+2y+1 = 4$. $x^2+y^2-4x+2y+1 = 0$. Thus,option $D$ is correct.

If the angle between a pair of tangents drawn from a point $P$ to the circle $x^2+y^2-4x+2y+3=0$ is $\frac{\pi}{2}$,then the locus of $P$ is

Similar Questions

The locus of the centres of the circles,which cut the circles $x^2+y^2+4x-6y+9=0$ and $x^2+y^2-5x+4y+2=0$ orthogonally,is

The number of pairs $(a, b)$ of positive real numbers satisfying $a^4+b^4 < 1$ and $a^2+b^2 > 1$ is

If the angle between a pair of tangents drawn from a point $P$ to the circle $x^2+y^2+4x-6y+9 \sin^2 \alpha+13 \cos^2 \alpha=0$ is $2 \alpha$,then the equation of the locus of $P$ is

$A$ rod $PQ$ of length $2a$ moves with its ends on the coordinate axes. Find the locus of the circumcenter of $\Delta OPQ$.

$A$ point moves such that its distance from the point $(-1, 0)$ is always three times its distance from the point $(0, 2)$. The locus of the point is

Vedclass Test Series

Exam Paper Generator

Online Exam Module