# Equation of Circle with (h,k) as Center

## Trending Questions

**Q.**The circle passing through (1, −2) and touching the axis of x at (3, 0) also passes through the point

- (−5, 2)
- (2, −5)
- (−2, 5)
- (5, −2)

**Q.**

The number of integral values of $k$ for which the line, $3x+4y=k$ intersects the circle, ${x}^{2}+{y}^{2}-2x-4y+4=0$ at two distinct points is

**Q.**

The circle passing through the intersection of the circles ${\mathrm{x}}^{2}+{\mathrm{y}}^{2}-6\mathrm{x}=0$ and, ${x}^{2}+{y}^{2}-4y=0$, having its center on the line, $2\mathrm{x}-3\mathrm{y}+12=0,$ also passes through the point:

$(-1,3)$

$(1,-3)$

$(-3,6)$

$(-3,1)$

**Q.**A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to the circle?

- 4x+3y−8=0
- 3x−4y−24=0
- 3x+4y−6=0
- 4x−3y+17=0

**Q.**

Find the equation of the circle which has its centre at the point (3, 4) and touches the straight line 5x+12y−1=0

**Q.**

The equation of the circle which touches x the axes of coordinates and the line x3+y4=1 and whose centres lie in the first quadrant is x2+y2−2cx−2cy+c2=0 where c is equal to

4

2

3

6

**Q.**Let differential equation of family of circles touching y−axis at the origin be dydx+x2−λy2μxy=0, where λ∈R, μ∈R−{0}. Then the value of λ+μ is

**Q.**

The equation of the smallest circle passing through the intersection of the line $x+y=1$ and the circle ${x}^{2}+{y}^{2}=9$ is

${x}^{2}+{y}^{2}+x+y-8=0$

${x}^{2}+{y}^{2}-x-y-8=0$

${x}^{2}+{y}^{2}-x+y-8=0$

None of these

**Q.**

Find the centre and radius of the circle *x*^{2} + *y*^{2} – 4*x* – 8*y* – 45 = 0

**Q.**

The line segment joining points$(4,7)$and $(-2,-1)$is the diameter of a circle. If the circle intersects the $X-$axis at$A$ and$B$, then$AB$ is equal to

$4$

$5$

$6$

$8$

**Q.**

Find the equation of a circle passing through the point (7, 3) having radius 3 units and whose centre lies on the line y=x−1.

**Q.**P is a point on the hyperbola x2a2−y2b2=1, N is the foot of the perpendicular from P on the transverse axis.The tangent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

**Q.**The locus of the centres of the circles, which touch the circle, x2+y2=1 externally, also touch the y−axis and lie in the first quadrant, is:

- y=√1+2x, x≥0
- y=√1+4x, x≥0
- x=√1+4y, y≥0
- x=√1+2y, y≥0

**Q.**

Equation of the circle through origin which cuts intercepts of length a and b on axes is

x2+y2−ax−by=0

none of these

x2+y2+ax+by=0

x2+y2+bx+ay=0

**Q.**

A circle has radius 3 units and its centre lies on the line y = x - 1. If it passes through the point (7, 3), find its equations.

**Q.**

Find the equation of the circle with centre (0, 2) and radius 2

**Q.**

The focal distance of a point on the parabola ${y}^{2}=16x$, whose ordinate is twice the abscissa, is

$6$

$8$

$10$

$12$

**Q.**

The point $(-4,5)$ is the vertex of a square and one of its diagonals is $7x-y+8=0$. The equation of the other diagonal is

$7x\u2013y+23=0$

$7y+x=30$

$7y+x=31$

$x\u20137y=30$

**Q.**

The equations of the circle which pass through the origin and make intercepts of lengths $4$ and $8$ on the $x$ and $y$ - axes respectively are

${x}^{2}+{y}^{2}\pm 4x\pm 8y=0$

${x}^{2}+{y}^{2}\pm 2x\pm 4y=0$

${x}^{2}+{y}^{2}\pm 8x\pm 16y=0$

${x}^{2}+{y}^{2}\pm x\pm y=0$

**Q.**

If $z=\left(\lambda +3\right)+i\sqrt{5-{\lambda}^{2}}$, then the locus of $z$ is a

circle

straight line

parabola

None of these

**Q.**

One diameter of the circle circumscribing the rectangle ABCD is 4y= x + 7.

If the coordinates of A and B are (-3, 4) and (5, 4) respectively, find the equation of the circle.

**Q.**The equation of the circle whose diameter lies on 2x + 3y = 3 and 16x - y = 4 which passes through (4, 6) is

- x2+y2−4x−8y=200
- 5(x2+y2)−4x=200
- x2+y2=40
- 5(x2+y2)−3x−8y=200

**Q.**If two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60∘. If the third side is 3, then the remaining fourth side is

- 2
- 3
- 4
- 5

**Q.**

Choose the correct statement about two circles whose equations are given below:

${x}^{2}+{y}^{2}\u201310x\u201310y+41=0$

${x}^{2}+{y}^{2}\u201322x\u201310y+137=0$

Circles have no meeting point.

Circles have two. meeting point

Circles have only one meeting point.

Circles have the same center.

**Q.**The equation of circle whose centre lies on 3x - y - 4 = 0 and x + 3y + 2 = 0 and has an area 154 square units is

- x2+y2−2x+2y−47=0
- x2+y2−2x+2y+47=0
- None of these
- x2+y2+2x−2y−47=0

**Q.**

Find the equation of a circle whose centre is (3, -1) and which cuts off a chord of length 6 units on the line 2x−5y+18=0.

**Q.**

Find the equations of the circles passing through two points on y-axis at distance 3 from the origin and having radius 5.

**Q.**The centre of a circle is (2, –3) and the circumference is 10π. Then the equation of the circle is

- x2+y2−4x+6y+12=0
- x2+y2+4x+6y+12=0
- x2+y2−4x+6y−12=0
- x2+y2−4x−6y−12=0

**Q.**If two adjacent vertices of a regular hexagon are (0, 0) and (1, 2), then equation of the circumcircle of the hexagon is

- x2+y2−x−2y=±3
- x2+y2−x−2y=±√3
- x2+y2−x−2y=±√3(2x−y)
- x2+y2−x−2y=0

**Q.**If a circle passes through the point A(1, 0), B(5, 0) and touches y−axis at C(0, h), then the value of h2 is