A pair of perpendicular lines passes through the origin and also through the points of intersection of the curve x² + y² = 4 with x + y = a, where a > 0. Then a is equal to

• 2

• 3

• 4

• 5

If 3x² - 11xy + 10y² - 7x + 13y + k = 0 denotes a pair of straight lines, then the point of intersection of the lines is

• (1, 3)

• (3, 1)

• (- 3, 1)

• (1, - 3)

163.

The number of points P(x, y) with natural numbers as coordinates that lie inside the quadrilateral formed by the lines 2x + y = 2, x = 0, y = 0 and x + y = 5 is

• 12

• 10

• 6

• 4

The image of the point (3, 8) in the line x + 3y = 7 is

• (1, 4)

• (4, 1)

• (- 1, - 4)

• (- 4, - 1)

The line joining the points A(2, 0) and B(3, 1) is rotated through an angle of 45°, about A in the anti-clockwise direction. The coordinates of B in the new position

• $\left(2, \sqrt{2}\right)$

• $\left(\sqrt{2}, 2\right)$

• (2, 2)

• $\left(\sqrt{2}, \sqrt{2}\right)$

If one of the lines in the pair of straight line given by 4x² + 6xy + ky² = 0 bisects the angle between the coordinate axes, then k ∈

• {- 2, - 10}

• {- 2, 10}

• {- 10, 2}

• {2, 10}

$$\begin{gathered} \mathrm{If} {\mathrm{ax}}^2 + 2\mathrm{hxy} +{\mathrm{by}}^2 + 2\mathrm{gx} + 2\mathrm{fy} + \mathrm{c} = 0 \\ \mathrm{represents} \mathrm{a} \mathrm{pair} \mathrm{of} \mathrm{parallel} \mathrm{lines}, \mathrm{then} \\ \sqrt{\frac{{\mathrm{g}}^2 - \mathrm{ac}}{{\mathrm{f}}^2 - \mathrm{bc}}}, \mathrm{is} \mathrm{equal} \mathrm{to} \end{gathered}$$

• $\frac{\mathrm{a}}{\mathrm{b}}$

• $\sqrt{\frac{\mathrm{a}}{\mathrm{b}}}$

• $\sqrt{\frac{\mathrm{b}}{\mathrm{a}}}$

• $\frac{\mathrm{b}}{\mathrm{a}}$

If s and p are respectively the sum and the product of the slopes of the lines 3x² - 2xy - 15y² = 0, then s: p is equal to

• 4 : 3

• 2 : 3

• 3 : 5

• 3 : 4

If the lines 3x + 4y - 14 = 0 and 6x + By + 7 = 0 are both tangents to a circle, then its radius is

• 7

• $\frac{7}{2}$

• $\frac{7}{4}$

• $\frac{7}{6}$

If the circle x² + y² + 8x - 4y + c = 0 touches the circle x² + y² + 2x + 4y - 11 = 0 externally and cuts the circle x² +y² - 6x + By + k = 0 orthogonally, then k is equal to

• 59

• - 59 

• 19

• - 19