A circle is drawn on the chord of a circle x² + y² = a² as diameter. The chord lies on the line x + y = a. What is the equation of the circle ? 

• ${\mathrm{x}}^2 + {\mathrm{y}}^2 - \mathrm{ax} - \mathrm{ay} + {\mathrm{a}}^2 = 0$

• ${\mathrm{x}}^2 + {\mathrm{y}}^2 - \mathrm{ax} - \mathrm{ay} = 0$

• ${\mathrm{x}}^2 + {\mathrm{y}}^2 + \mathrm{ax} +\hspace{0.17em}\mathrm{ay} = 0$

• ${\mathrm{x}}^2 + {\mathrm{y}}^2 +\hspace{0.17em}\mathrm{ax} + \mathrm{ay} - 2{\mathrm{a}}^2 = 0$

The equation 2x² - 3y² - 6 = 0 represents : 

• a circle

• a parabola

• an ellipse 

• a hyperbola

The two parabolas y² = 4ax and x² = 4ay intersect :

• at two points on the line y = x

• Only at the origin

• At three points one of which lies on y + x = 0

• Only at (4a, 4a)

The circle  x² + y² + 4x - 7y + 12 = 0, cuts an intercepton y-axis equal to :

• 1

• 3

• 4

• 7

In a circle of diameter 44 cm, the length of a chord is 22 cm. What is the length of minor arc of the chord ?

• $\frac{484}{21} \mathrm{cm}$

• $\frac{242}{21}\mathrm{cm}$

• $\frac{121}{21}\mathrm{cm}$

• $\frac{44}{7}\mathrm{cm}$

The sum of the focal distance of a point on an ellipse is constant and equal to the :

• Length of minor axis

• Length of major axis

• Length if latus rectum

• Sum of the lengths of semi-major and semi-minor axes

For $\mathrm{r} > 0$, f(r) is the ratio of perimeter to area of a circle of radius r. Then f(1) + f(2) = ?

• 1

• 2

• 3

• 4

8.

The minimum distance from the point (4, 2) to y = 8x is equal to :

• $\sqrt{2}$

• $2\sqrt{2}$

• 2

• $3\sqrt{2}$

What is the equation of the ellipse whose vertices are(± 5, 0) and foci are at (± 4, 0) ?

• $\frac{{\mathrm{x}}^2}{25} + \frac{{\mathrm{y}}^2}{9} = 1$

• $\frac{{\mathrm{x}}^2}{16} + \frac{{\mathrm{y}}^2}{9} = 1$

• $\frac{{\mathrm{x}}^2}{25} + \frac{{\mathrm{y}}^2}{16} = 1$

• $\frac{{\mathrm{x}}^2}{9} + \frac{{\mathrm{y}}^2}{25} = 1$

What is the area of the region bounded the paraoolas y² = 6(x - 1) and y² = 3x ?

• $\frac{\sqrt{6}}{3}$

• $\frac{2\sqrt{6}}{3}$

• $\frac{4\sqrt{6}}{3}$

• $\frac{5\sqrt{6}}{3}$