2. Find the length of the chord of the circle x2 + y2 = a2 on the line x cos α + y sin α = p.

3. If x2 + y2 + 4x + 8 = 0 and x2 + y2 − 16y + k = 0 represent two orthogonal circles, then find k.

4. If one end of the focal chord of the parabola y2 = 8x is ( 1−2, 2) find the other end.

5. If 3x − 4y + k = 0 is the tangent to the hyperbola x2 − 4y2 = 5, then find k.

6. Show that the line x + y + 1 = 0 touches the circle x2 + y2 − 3x + 7y + 14 = 0. Also find the point of contact.

7. If the line 2x + 3y = 1 cuts the circle x2 + y2 = 4 in A and B, find the equation of the circle with AB as diameter.

8. Find the equation of the tangent to the ellipse 9x2 + 16y2 = 144 and which makes equal intercepts on the coordinate axes.

9. Obtain the differential equation which corresponds to each of the following family of curves:

i) The circles which touch the Y - axis at the origin.

ii) The parabolas having their foci at the origin and axis along the X - axis.

11. Find the locus of mid points of the chords of contact of x2 + y2 = a2 from the points lying on the line lx + my + n = 0.

12. Find the equations of all common tangents to the circles x2 + y2 = 9 and x2 + y2 − 16x + 2y + 49 = 0.

13. Show that the equations of common tangents to the circle x2 + y2 = 2a2 and the parabola y2 = 8ax are y = ± (x + 2a).

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