The number of common tangents to the two circles x² + y - 8x + 2y = 0 and x² + y² - 2x - 16y + 25 = 0 is :

• 1

• 2

• 3

• 4

Observe the following statements :

I. The circle x² + y² - 6x - 4y - 7 = 0 touches y-axis.

II. The circle x² + y² + 6x + 4y - 7 = 0 touches

x-axis. Which of the following is a correct statement ?

• Both I and II are true

• Neither I nor II is true

• I is true, II is false

• I is false, II is true

The length of the tangent drawn to the circle x² + y² - 2x + 4y - 11 = 0

• 1

• 2

• 3

• 4

Equations of the latus rectum of the ellipse

9x² + 4y² - 18x - 8y - 23 = 0 are : 

• $\mathrm{y} = \pm \sqrt{5}$

• $\mathrm{x} = \pm \sqrt{5}$

• $\mathrm{y} = 1 \pm \sqrt{5}$

• $\mathrm{x} = - 1 \pm \sqrt{5}$

The equation of the circle of radius 3 that lies in the fourth quadrant and touching the lines x = 0 and y = 0 is

• x² + y² - 6x + 6y + 9 = 0

• x² + y² - 6x - 6y + 9 = 0

• x² + y² + 6x - 6y + 9 = 0

• x² + y² + 6x + 6y + 9 = 0

The inverse point of (1, 2) with respect to the circle

x² + y² - 4x - 6y + 9 = 0 is

• (0, 0)

• (1, 0)

• (0, 1)

• (1, 1)

287.

For the parabola y² + 6y - 2x + 5 = 0

(I) The vertex is (- 2, - 3)

(II) The directrix is y + 3 = 0

Which of the following is correct ?

• Both I and II are true

• I is true, II is false

• I is false, II is true

• Both I and II are false

The value of k, If (1, 2), (k, - 1) are conjugate points with respect to the ellipse 2x² + 3y² = 6 is

• 2

• 4

• 6

• 8

If the line lx + my = 1 is a normal to the hyperbola

$\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2} - \frac{{\displaystyle {\mathrm{y}}^2}}{{\mathrm{b}}^2} = 1, \mathrm{then} \frac{{\mathrm{a}}^2}{{\mathrm{l}}^2} - \frac{{\mathrm{b}}^2}{{\mathrm{m}}^2} \mathrm{is} \mathrm{equal} \mathrm{to}$

• a² - b²

• a² + b²

• (a² + b²)²

• (a² - b²)²

If the lines 2x - 3y = 5 and 3x - 4y = 7 are two diameters of a circle of radius 7, then the equation of the circle is

• x² + y² + 2x - 4y - 47 = 0

• x² + y² = 49

• x² + y² - 2x + 2y - 47 = 0

• x² + y² = 17