Question

If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1= 0 intersect in two distinct points P and Q then the line

5x + by – a = 0 passes through P and Q for:  

Solution

Correct option is

No value of a

PQ is the common chord of the two circles whose equation is given by S1 – S2 = 0 or 5ax + (c – dy + (a + 1) = 0.

Compare with given line PQ.   

        5x + by – a = 0  

  

Above gives only imaginary values of a, i.e., no real values of a.

SIMILAR QUESTIONS

Q1

The distance between the chords of contact of the tangent to the circle x2 + y2 + 2gx + 2fy + c = 0 from the origin and the point (gf) is

Q2

The angle between the tangents drawn from the origin to the circle (x – 7)2 + (y + 1)2 = 25 is

Q3

A square is inscribed in the circle x2 + y2 – 2x + 4y + 3 = 0. Its sides are parallel to the co-ordinates axes. Then one vertex of the square is

Q4

If the lines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area 49π square units, then the equation of the circle is:

Q5

A variable circle passes through a fixed point A(pq) and touches the x-axis. The locus of the other end of the diameter through A is:

Q6

A circle touches the x-axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is:

Q7

The triangle PQR is inscribed in the circle x2 + y2 = 25. If Q and R have co-ordinates (3, 4) and (–4, 3) respectively than QPR is equal  to

Q8

Let AB be a chord of the circle x2 + y2 = a2 subtending a right angle at the centre. Then the locus of the centroid of the triangle PAB as Pmoves on the circle is

Q9

The lines joining the origin to the points of intersection of the line 4x + 3y = 24 with the circle (x – 3)2 + (y – 4)2 = 25 are

Q10

The intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle on AB as diameter is: