If P₁, P₂, P₃ are the perimeters of the three circles 

x² + y² + 8x - 6y = 0, 4x² + 4y - 4x - 12y - 186 = 0 and x² + y - 6x + 6y - 9 = 0 respectively, then

• ${\mathrm{P}}_1 < {\mathrm{P}}_2 < {\mathrm{P}}_3$

• ${\mathrm{P}}_1 < {\mathrm{P}}_3 < {\mathrm{P}}_2$

• ${\mathrm{P}}_3 < {\mathrm{P}}_2 < {\mathrm{P}}_1$

• ${\mathrm{P}}_2 < {\mathrm{P}}_3 < {\mathrm{P}}_1$

If the line 3x - 2y + 6 = 0 meets X-axis and Y-axis, respectively at A and B, then the equation of the circle with radius AB and centre at A is

• x² + y² + 4x + 9 = 0

• x² + y² + 4x - 9 = 0

• x² + y² + 4x + 4 = 0

• x² + y² + 4x - 4 = 0

A line l meets the circle x² + y² = 61 in A, B and P(- 5, 6) is such that PA = PB = 10. Then,the equation of l is

• 5x + 6y + 11 = 0

• 5x - 6y - 11 = 0

• 5x - 6y + 11 = 0

• 5x - 6y + 11 = 0

If (1, a), (b, 2) are conjugate points with respect to the circle x² + y² = 25, then 4a + 2b is equal to

• 25

• 50

• 100

• 150

The eccentricity of the conic 36x² + 144y² - 36x - 96y -119 = 0 is

• $\frac{\sqrt{3}}{2}$

• $\frac{1}{2}$

• $\frac{\sqrt{3}}{4}$

• $\frac{1}{\sqrt{3}}$

The polar equation $\cos \left(\mathrm{\theta }\right) + 7\sin \left(\mathrm{\theta }\right) = \frac{1}{\mathrm{r}}$ represents a

• circle

• parabola

• straight line

• hyperbola

The centre of the circle ${\mathrm{r}}^2 - 4\mathrm{r}\left(\cos \left(\mathrm{\theta }\right) + \sin \left(\mathrm{\theta }\right)\right) - 4 = 0$ in cartesian coordinates is

• (1, 1)

• (- 1, - 1)

• (2, 2)

• (- 2, - 2)

298.

The radius of the circle r = $\sqrt{3}\sin \left(\mathrm{\theta }\right) + \cos \left(\mathrm{\theta }\right)$ is

• 1

• 2

• 3

• 4

The equation of the circle whose diameter is the common chord of the circles x² + y² + 2x + 3y + 2 = 0 and x² + y² + 2x - 3y - 4 = 0 is

• x² + y² + 2x + 2y + 2 = 0

• x² + y² + 2x + 2y - 1 = 0

• x² + y² + 2x + 2y + 1 = 0

• x² + y² + 2x + 2y + 3 = 0

If x - y + 1 = 0 meets the circlex² + y² + y - 1 = 0 at A and B, then the equation of the circle with AB as diameter is

• 2(x² + y²) + 3x - y + 1 = 0

• 2 (x² + y²) + 3x - y + 2 = 0

• 2(x² + y²) + 3x - y + 3 = 0

• x² + y² + 3x - y + 1 = 0