# Equation of the Circle Using End Points of Diameter

## Trending Questions

**Q.**

The equation of the circumcircle of an equilateral triangle is ${x}^{2}+{y}^{2}+2gx+2fy+c=0$ and one vertex of the triangle is $\left(1,1\right)$ . The equation of incircle of the triangle is

$4\left({x}^{2}+{y}^{2}\right)={g}^{2}+{f}^{2}$

$4\left({x}^{2}+{y}^{2}\right)+8gx+8fy=\left(1-g\right)\left(1+3g\right)+\left(1-f\right)\left(1+3f\right)$

$4\left({x}^{2}+{y}^{2}\right)+8gx+8fy={g}^{2}+{f}^{2}$

None of these

**Q.**Equation of the circle passing through (4, 3) and centre at the origin is _______ .

- (x−4)2+(y−3)2=7
- x2+y2=25
- x2+y2=49
- (x−3)2+(y−4)2=25

**Q.**

Find the coordinates of the centre of the circle passing through the points (0, 0), (–2, 1) and (–3, 2). Also, find its radius. [4 MARKS]

**Q.**

The radius of the circle x2 + y2 − 2x + 4y − 11 = 0

is

- -1 units
- 2 units
- 11 units
- 4 units

**Q.**

Consider the points A(3, 2), B(9, 4), C(7, 10). Then the circle with AC as diameter doesn't pass through B.

False

True

**Q.**Find the radius of the circle x2 + y2 − 2x + 4y − 11 = 0.

- 4

**Q.**

The equation of the circle having (−2, 1) and (4, −1) as the endpoints of its diameter is

x2+y2−2x−9=0

x2+y2−2x+9=0

x2+y2+2x+9=0

x2+y2+2x−9=0

**Q.**

Consider the points A(4, 3) and B(0, 1). If a circle is drawn with AB as diameter, then the coordinates of the points where this circle intersects the x-axis are

(−3, 0) and (2, 0).

(3, 0) and (−1, 0).

(3, 0) and (1, 0)

(2, 0) and (−1, 0).

**Q.**

A circle is drawn with AB as the diameter whose endpoints are A(2, 4) and B(4, 12). If another circle with diameter one-third of the above circle is drawn with the same centre, what are the points that the circle cuts AB?

(6, 283) and (6, 203)

(10, 283) and (6, 203)

(10, 283) and (10, 203)

(10, 203) and (6, 203)

**Q.**

The equation of the circle having (−2, −1) and (2, 1) as the endpoints of its diameter is

x2+y2=5

x2−y2=5

x2+y2=−5

x2−y2=−5

**Q.**Question 14

If the centre of a circle is (2a, a-7), then find the values of a , if the circle passes through the point (11, -9) and has diameter 10√2 units.

**Q.**

The equation of circle with centre (1, 1) and radius 4 is given by (x−1)2 + (y−1)2 = 4

True

False

**Q.**

A circle is drawn with AB as the diameter whose endpoints are A(2, 4) and B(4, 12). If another circle with diameter one-third of the above circle is drawn with the same centre, what are the points that the circle cuts AB?

(6, 283) and (6, 203)

(10, 283) and (6, 203)

(10, 283) and (10, 203)

(10, 203) and (6, 203)

**Q.**The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmoharare planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the Fig. The students are to sow seeds of flowering plants on the remaining area of the plot.

(i) Taking A as origin, find the coordinates of the vertices of the triangle.

(ii) What will be the coordinates of the vertices of ΔPQR if C is the origin?

Also calculate the areas of the triangles in these cases. What do you observe?

**Q.**

The equation of the circle having (3, 3) and origin as the endpoints of its diameter is

x2+y2−3(x+y)=0

x2+y2−3x+y=0

(x+y)2−2xy−3(x+y)=0

(x+y)2+2xy−3x+y=0

**Q.**Find the center of the circle given by the equation x2+y2−4x+6y−51=0.

- (3, -2)
- (-3, 2)
- (2, -3)
- (-2, 3)

**Q.**How are the points (−2, 2), (2, 3) and (2, −3) situated with respect to the circle x2+y2−4x–2y+3=0

**Q.**A(−3, 9) and B(9, −1) are the endpoints of the diameter of a circle. The equation for this circle is

- (x−3)2+(y−4)2=61
- (x−7)2+(y+4)2=269
- (x+7)2+(y−4)2=61
- (x+3)2+(y+4)2=169
- (x+3)2+(y−4)2=25

**Q.**If the origin is shifted to the point (1, 1), axes remaining parallel, find the new equation of the locus in each of the following.

i) xy−x−y+1=0

ii) x2−y2−2x+2y=0

iii) x2+y2−4x+6y+3=0

**Q.**

The equation of the circle having (6, 7) and (4, 3) as the endpoints of its diameter is

(x+y)2−2xy+45=0

(x2−y2−2xy+45=0

10(x+y)−2xy+45=0

(x+y)[(x+y)−10]−2xy+45=0

**Q.**

Equation of the circle passing through (2, 3) and centre at the origin is _______ .

(x−2)2+(y−3)2=13

x2+y2=13

(x−3)2+(y−2)2=13

x2−y2=13

**Q.**

The equation of the circle having (4, −1) and (2, −1) as the endpoints of its diameter is

x2+y2−x+2y+9=0

x2+y2−6x+2y−9=0

x2+y2+x+y−9=0

x2+y2−6x+2y+9=0

**Q.**

Find the radius of the circle x2 + y2 − 2x + 4y − 11 = 0

**Q.**Equation of the circle passing through (2, 3) and centre at the origin is

- x2+y2=13
- x2+y2=12
- x2+y2=11
- x2+y2=1

**Q.**Find the equation of the circle when the end points of a diameter are A(3, 2) and B(3, 5)

**Q.**Compare the given equation of the circle and then find the value of a+b+c+d+e if the centre of the circle is at origin (2, 0) and radius is 6.

given equation : ax2+by2+cx+dy+e=0

**Q.**If (6, −3) is the one extremity of diameter to the circlex2+y2−3x+8y−3=0 then its other extremity is -

- (3, −5)
- (32, −4)
- (−3, −5)
- (3, 5)

**Q.**

The equation of the circle having (4, 2) and (2, −12) as the end points of its diameter is

x2+y2+6x+10y+16=0

x2+y2−6x+10y−16=0

x2+y2+10x−6y+16=0

x2+y2−10x+6y−16=0

**Q.**Find the center of the circle given by the equation x2+y2−4x+6y−51=0.

**Q.**Find the centre and the radius of the circle which is concentric to the circle x2+y2−16=0 having radius double of the radius of the given circle.