#### Analytical Geometry Two Marks Question

11th Standard

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Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. Find the equation of the following circles having the center ( 0,0) and radius 2 units

2. Find the centre and radius of the circle x2 + y2 = 16

3. Find the center and radius of the circle (x + 2) ( x - 5) + (y -2 ) ( y -1) = 0

4. Find the equation of the circle whose centre is (-3, -2) and having circumferences 16$\pi$

5. Find the equation of the circle on the line joining the points (1,0), (0,1) and having its centre on the line x + y= 1

6. If the lines x+ y = 6 and x + 2y = 4 are diameters of the circle , and the circle passes through the point (2,6)  then find its equation.

7. Convert the parabola y2=4x+4y into standard form.

8. Convert the equation of the parabola x2+y=6x-14 into the standard form.

9. Find the focus, equation of the directrix, vertrix and length of latus sections of the parabola x2=6y.

10. Show that perpendicular distances of the line x-y+5=0 from origin and from the point P(2, 2) are equal.

11. If the angle between the two lines is $\frac{\pi}{4}$ and slope of one of the lines is 3, then find the slope of the other line.

12. Find the equation of the circle with centre at (3, –1) and radius is 4 units.

13. Find the equation of the circle with centre at origin and radius is 3 units.

14. Find the parametric equations of the circle x2+y2=25

15. The supply of a commodity is related to the price by the relation x=$\sqrt{5p-15}$ . Show that the supply curve is a parabola.