The points situated on the line x + y = 4 whose distance fromthe line 4x + 3y = 10 is unity, are

• (3, 1), (- 7, 11)

• (3, 1), (7, 11)

• (- 3, 11), (- 7, 11)

• (1, 3), (- 7, 11)

Lines represented by the pair ofstraight lines ab (x² - y²) +(a² - b²)y = 0, are

• ax - by = 0, bx + ay = 0

• ax - by = 0, bx - ay = 0

• ax + by = 0, bx + ay = 0

• ax + by = 0, bx - ay = 0

Angle between the pair of straight lines (x² + y²) sin²($\mathrm{\alpha }$) = $\left(\mathrm{xcos}\left(\mathrm{\theta }\right) - \mathrm{ysin}\left(\mathrm{\theta }\right)\right)$² is

• $\mathrm{\alpha }$

• $2\mathrm{\alpha }$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

The pair of straight lines joining the origin to the points of intersection of the line y = $2\sqrt{2}$x + c and the circle x² + y² = 2, are at right angles, if

• c² - 4 = 0

• c² - 8 = 0

• c² - 9 = 0

• c² - 10 = 0

If the ratio of gradients ofthe lines represented by ax² + 2hxy + by = 0 is 1 : 3, then the value of  the ratio h² : ab is

• 1 : 3

• (1, 1)

• 4 : 3

• 1 : 1

If the equations of the opposite sides of a parallelogram are x² - 7x + 6 = 0 and y² - 14y + 40 = 0, then the equation of one of its diagonal will be

• 6x + 5y + 14 = 0

• 6x - 5y + 14 = 0

• 5x + 6y + 14 = 0

• 5x - 6y - 14 = 0

From the point P (16, 7), tangents PQ and PR are drawn to the circle x² + y² - 2x - 4y - 20 = 0. If C is the centre of the circle, then area of the quadrilateral PQCR is

• 15 sq unit

• 50 sq unit

• 75 sq unit

• 150 sq unit

18.

Tangents are drawn from any point of the circle x² + y² = a² to the circle x² + y² = b². If the chord of contact touches the circle x² + y² = c², then

• a, b, c are in AP

• a, b, c are in GP

• a, b, c are in HP

• a, b, c are in GP

The equation of tangents to the circle x² + y² = 4, which are parallel to x + 2y + 3 = 0, are

• $\mathrm{x} + 2\mathrm{y} = \pm 2\sqrt{3}$

• $\mathrm{x} - 2\mathrm{y} = \pm 2\sqrt{5}$

• $\mathrm{x} - 2\mathrm{y} = \pm 2\sqrt{3}$

• $\mathrm{x} + 2\mathrm{y} = \pm 2\sqrt{5}$

Equation of the circle, which passes through (4, 5) and whose centre is (2, 2), is

• x² + y² + 4x + 4y - 5 = 0

• x² + y² - 4x - 4y - 5 = 0

• x² + y² - 4x = 13

• x² + y² - 4x - 4y + 5 = 0