Question

Find the equation of the circle whose centre is the point of intersection of the lines 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 and passes through the origin.

Solution

Correct option is

 

The point of intersection of the lines 2x – 3y + 4 = 0 and

3x + 4y – 5 = 0 is 

Therefore, the centre of the circle is at 

Since the origin lies on the circle, its distance from the centre of the circle is radius of the circle, therefore,

               

               

SIMILAR QUESTIONS

Q1

Find the equation of the normal to the circle x2 + y2 = 2x, which is parallel to the line x + 2y = 3.

Q2

 

Find the equation of the circle which cuts orthogonally each of the three circles given below: 

x2 + y2 – 2x + 3y – 7 = 0, x2 + y2 + 5x – 5y + 9 = 0 and x2 + y2 + 7x – 9x + 29 = 0.

Q3

Circum centre of the triangle PT1T2 is at

Q4

If P is taken to be at (h, 0) such that P’ lies on the circle, the area of the rhombus is

Q5

Locus of mid-point of the chords of contact of x2 + y2 = 2 from the points on the line 3x + 4y = 10 is a circle with centre P. If O be the origin then OP is equal to

Q6

Suppose ax + bx + c = 0, where abc are in A.P. be normal to a family or circles. The equation of the circle of the family which intersects the circle x2 + y2 – 4x – 4y – 1 = 0 orthogonally is

Q7

Find the equation of chord of x2 + y2 – 6x + 10y – 9 = 0 which is bisected at (–2, 4).

Q8

Find the equation of that chord of the x2 + y2 = 15 which is bisected at (3, 2).

Q9

 

Find the centre and radius of the circle 

             2x2 + 2y2 = 3x – 5y + 7

Q10

Find the equation of the circle concentric with the circle x2 + y2 – 8x + 6y– 5 = 0 and passing through the point (–2, –7).