An arch is in the form of a parabola with its vertical. The arch is 10 m high and 5 m wide at the base. How wide it is 2 m from the vertex of the parabola?

5

(a)

The foci of a hyperbola coincide with the faci of the elipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { y^{ 2 } }{ 9 } =1\) find the equation of the hyperbola if its eccentricity is 2.

5

(a)

Find the equation of the hyperbola satisfying the given conditions.
Foci (0, ± \(\sqrt10\) ),passing through (2, 3)

5

(a)

A rod of length 12cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

5

(a)

Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x +y = 16.

5

(a)

Find the equation of the circle passing through the points (2,3) and (-1, 1) and whose centre is on the line x - 3y - 11 =0.

5

(a)

Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the point (2,3).

5

(a)

Find the equation of the circle passing through (0, 0) and making intercepts a and b on the coordinate axes.

5

(a)

Find the equation of the parabola whose vertex is at (2,1) and the directrix x = y = 1

5

(a)

A man running a race leave no space course notes that the sum of the distances from the two flag posts from him is always 10m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.

5

(a)