$$\begin{gathered} \mathrm{The} \mathrm{equation} \mathrm{of} \mathrm{the} \mathrm{radical} \mathrm{axis} \mathrm{of} \mathrm{the} \mathrm{pair} \mathrm{of} \mathrm{circles} \\ 7{\mathrm{x}}^2 + 7{\mathrm{y}}^2 - 7\mathrm{x} + 14\mathrm{y} + 18 = 0 \mathrm{and} 4{\mathrm{x}}^2 + 4{\mathrm{y}}^2 - 7\mathrm{x} + 8\mathrm{y} + 20 = 0 \mathrm{is} \end{gathered}$$

• x - 2y - 5 = 0

• 2x - y + 5 = 0

• 21x - 68 = 0

• 23x - 68 = 0

$$\begin{gathered} {\mathrm{x}}^2 + {\mathrm{y}}^2 - 8\mathrm{x} + 40 = 0 \\ 5{\mathrm{x}}^2 + 5{\mathrm{y}}^2 -25\mathrm{x} + 80 = 0 \\ {\mathrm{x}}^2 + {\mathrm{y}}^2 - 8\mathrm{x} + 16\mathrm{y} + 160 = 0 \\ \mathrm{From} \mathrm{the} \mathrm{point} \mathrm{P} \mathrm{are} \mathrm{equal}, \mathrm{then} \mathrm{P} = ? \end{gathered}$$

• $\left(8, \frac{15}{2}\right)$

• $\left(- 8, \frac{15}{2}\right)$

• $\left(8, \frac{- 15}{2}\right)$

• $\left(- 8, \frac{- 15}{2}\right)$

The equation of the circle concentric with the circle x² + y² - 6x + 12y + 15 = 0 and of double its area is

• x² + y² - 6x +12y - 15 = 0

• x² + y² - 6x +12y - 30 = 0

• x² + y² - 6x +12y - 25 = 0

• x² + y² - 6x +12y - 20 = 0

If the circle x² + y² + 2x + 3y + 1 = 0 cuts another circle x² + y² + 4x + 3y + 2 = 0 in A and B, then the equation of the circle with AB as a diameter is

• x² + y²  + x + 3y + 1 = 0

• 2x² + 2y²  + 2x + 6y + 1 = 0

• x² + y²  + x + 6y + 1 = 0

• 2x² + 2y²  + x + 3y + 1 = 0

The equation of the hyperbola which passes through the point (2, 3) and has the asymptotes 4x + 3y - 7 = 0 and x - 2y - 1 = 0 is

• 4x² + 5xy - 6y² - 11x + 11y + 50 = 0

• 4x² + 5xy - 6y² - 11x + 11y - 43 = 0

• 4x² - 5xy - 6y² - 11x + 11y + 57 = 0

• x² - 5xy - y² - 11x + 11y - 43 = 0

The product of the perpendicular distances from any point on the hyperbola $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2} - \frac{{\mathrm{y}}^2}{{\mathrm{b}}^2} = 1$ to its asymtotes is

• $\frac{{\mathrm{a}}^2{\mathrm{b}}^2}{{\mathrm{a}}^2 - {\mathrm{b}}^2}$

• $\frac{{\mathrm{a}}^2{\mathrm{b}}^2}{{\mathrm{a}}^2 + {\mathrm{b}}^2}$

• $\frac{{\mathrm{a}}^2 + {\mathrm{b}}^2}{{\mathrm{a}}^2{\mathrm{b}}^2}$

• $\frac{{\mathrm{a}}^2 - {\mathrm{b}}^2}{{\mathrm{a}}^2{\mathrm{b}}^2}$

If the lines 2x + 3y +12 = 0, x - yy + k = 0 are conjugate with respect to the parabola y² = 8x, then k is equal to

• 10

• $\frac{7}{2}$

• - 12

• - 2

Find the equation to the parabola, whose axis parallel to they-axis and which passes through the points (0, 4), (1, 9) and (4, 5) is

• y = - x² + x + 4

• y = - x² + x + 1

• $\mathrm{y} = \frac{- 19}{12}{\mathrm{x}}^2 + \frac{79}{12}\mathrm{x} + 4$

• $\mathrm{y} = \frac{- 19}{12}{\mathrm{x}}^2 + \frac{89}{12}\mathrm{x} + 4$

If the line y = 2x + c is a tangent to the circle x² + y² = 5, then a value of

• 2

• 3

• 4

• 5

540.

A line segment AM = a moves in the XOY plane such that AM is parallel to the X-axis. If A moves along the circle x² + y² = a², then the locus of M is

• x² + y² = 4a²

• x² + y² = 2ax

• x² + y² = 2ay

• x² + y² = 2ax + 2ay