Sample QuestionsCircles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the equation of a circle is $\lambda x^2+(2 \lambda-3) y^2-4 x+$ $6 y-1=0$, then coordinates of centre are
- A
$\left(\frac{4}{3},-1\right)$
- ✓
$\left(\frac{2}{3},-1\right)$
- C
$\left(-\frac{2}{3}, 1\right)$
- D
$\left(\frac{2}{3}, 1\right)$
Answer: B.
View full solution →The position of the point $(5,7)$ with respect to the circle, $x^2+y^2=100$ is
Answer: A.
View full solution →The value of $\lambda$ for which the equation $2\left(x^2+y^2\right)-$ $6 x+8 y+\lambda=0$ represents a point circle is
- A
$\frac{25}{4}$
- B
$\frac{4}{25}$
- ✓
$\frac{25}{2}$
- D
$\frac{2}{25}$
Answer: C.
View full solution →If one end of a diameter of the circle $x^2+y^2-4 x-$ $6 y+11=0$ is $(3,4)$, then the coordinates of other end of the diameter is
- ✓
$(1,2)$
- B
$(2,1)$
- C
$(-1,2)$
- D
$(2,-1)$
Answer: A.
View full solution →The equation of the circle which touches $x$-axis and whose centre is $(1,2)$ is
- A
$x^2+y^2-2 x+4 y+1=0$
- B
$x^2+y^2+2 x-4 y+1=0$
- ✓
$x^2+y^2-2 x-4 y+1=0$
- D
$x^2+y^2-2 x-4 y-1=0$
Answer: C.
View full solution →Find the equation of the circle with centre $C(-2,3)$ and which touches the line $x-y+7=0$.
View full solution →If a circle passes through the points $(0,0),(a, 0)$ and $(0, b)$, then find the coordinates of its centre.
View full solution →A circle of radius $r$ is in the second quadrant. If the circle touches both the axes, then find the equation of the circle.
View full solution →Find the parametric equations of the circle $x^2+y^2-2 x+4 y-4=0$.
View full solution →Find the equation of the circle which passes through the point of intersection of the circles $x^2+y^2+2 x+3 y-7=0$ and $x^2+y^2-6 x+2 y-5=0$ and through the point $(2,-3)$.
View full solution →Prove that the circles
$x^2+y^2+2 a x+c=0 \text { and } x^2+y^2+2 b y+c=0$
will touch each other, if
$\frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{c}$
View full solution →Find the length of the chord intercepted by the circle $x^2+y^2-6 x+8 y-5=0$ on the line $2 x-y=5$.
View full solution →Find the equation of the circle which passes through the points $(0,3)$ and $(5,2)$ and whose centre lies on the $x$-axis.
View full solution →If $l x+m y= 1$ touches the circle $x^2+y^2=a^2$ then prove that the point $(l, m)$ lies on the circle $x^2+y^2$ $=a^{-2}$.
View full solution →Find the equations of the circle passing through the point $A(-4,2)$ and touching the lines $x+y=2$ and $x-y=2$.
View full solution →Show that the points $(7,5),(6,-2),(-1,-1)$ and $(0,6)$ are concyclic. Also, find the radius and the centre of the circle on which they lie.
View full solution →Find the equation of the circle passing through the vertices of a triangle whose sides are represented by the equations $x+y=2,3 x-4 y=6$ and $x-y=$ 0.
View full solution →$A(1,0)$ and $B(7,0)$ are two points on the axis of $X$. A point $P$ is taken in the first quadrant such that $P A B$ is an isosceles triangle and $P B=5$ units. Find the equation of the circle described on $P A$ as diameter.
View full solution →The centre of a circle is in the first quadrant and the circle touches the $y$-axis at the point $(0,2)$ and passes through the point $(1,0)$. Find the equation of the circle.
View full solution →Circle $x^2+y^2=9$ and $x^2+y^2+8 y+c=0$ will touch externally if $c=$ _________________ .
View full solution →Equation $a x^2+b y^2+2 h x y+2 g x+2 f y+c=0$ will represent a circle, if _________________ .
View full solution →The straight line $y=m x+c$ will touch the circle $x^2+y^2=a^2$, if $c=$ _________________ .
View full solution →If the circle $x^2+y^2-3 x+ k y-5=0$ and $4 x^2+4 y^2$ $-12 x-y-9=0$ be concentric, then $k=$ _________________ .
View full solution →The value of ' $p$ ' so that the equation $x^2+y^2-2 p x$ $+4 y-12=0$ may represent a circle of radius 5 units is _________________ .
View full solution →Find the equation of circle which passes through the points $(0,2),(3,0)$ and $(3,2)$. Find also the centre and radius of this circle.
View full solution →Find the equation of the circle which passes through $(1,-2)$ and $(4,-3)$ and whose centre lies on the line $3 x+4 y=7$
View full solution →Find the equation of circle concentric with circle $4 x^2+4 y^2-12 x-16 y-21=0$ and half its area.
View full solution →Whatever be the value of $t$, prove that the locus of the point of intersection of the lines $x \cos t+y \sin t$ $=a$ and $x \sin t-y \cos t=b$ is a circle.
View full solution →(i) Find the shortest distance of the point $(8,1)$ from the circle $(x+2)^2+(y-1)^2=25$.
(ii) Find the farthest distance of the point $(1,5)$ from the circle $(x-1)^2+(y+1)^2=16$.
View full solution →Let the equation of circle whose centre is $(h, k)$ and radius is ' $a$ ' is given by
$(x-h)^2+(y-k)^2=a^2$
Then match the following columns.| Column - l | Column - ll |
| (a) Equation of circle whose centre is at $x$-axis and origin is not on the circumference of the circle. | (i) $x^2+y^2-2 x y=0$ |
| (b) Equation of circle whose centre is at $y$-axis and origin is not on the circumference of the circle. | (ii) $x^2+(y-k)^2=a^2$ |
| (c) Equation of circle whose centre is on the $x$-axis and origin is on the circumference of the circle. | (iii) $x^2+y^2-2 a x=0$ |
| (d) Equation of circle whose centre is on the $y$-axis and origin is on the circumference of the circle. | (iv) $(x-h)^2+y^2=a^2$ |
View full solution →Let the equation of circle whose centre is $(h, k)$ and radius is ' $a$ ' is given by
$(x-h)^2+(y-k)^2=a^2$
Then match the following columns.| Column - l | Column - ll |
| (a) Equation of circle whose centre is at $x$-axis and origin is not on the circumference of the circle. | (i) $x^2+y^2-2 x y=0$ |
| (b) Equation of circle whose centre is at $y$-axis and origin is not on the circumference of the circle. | (ii) $x^2+(y-k)^2=a^2$ |
| (c) Equation of circle whose centre is on the $x$-axis and origin is on the circumference of the circle. | (iii) $x^2+y^2-2 a x=0$ |
| (d) Equation of circle whose centre is on the $y$-axis and origin is on the circumference of the circle. | (iv) $(x-h)^2+y^2=a^2$ |
View full solution →