Find the locus of a point which divides so that the sum of its distances from (-4, 0) and (4, 0) is 10 units.

For the ellipse x² + 3y² = a², find the length of major and minor axis.

Find the eccentricity of the ellipse with foci on x-axis if its latus rectum be equal to one half of its major axis.

Find the eccentricity of the hyperbola with foci on the x-axis if the length of its conjugate axis is \({ \left( \frac { 3 }{ 4 } \right) }^{ th }\) of the length of its tranverse axis.

Find the equation of the hyperbola whose vertices are (0, ±7) and e = \(\frac { 4 }{ 3 } \)

Find the length of the tangent from (2, 3) to the circle \(x^{2}+y^{2}-4 x-3 y+12=0\)

Show that the point (2, 3) Iies inside the circle \(x^{2}+y^{2}-6 x-8 y+12=0\)

Find the equation of the tangent to the circle \(x^{2}+y^{2}=25\) at (4, 3).

If y = 3x + c is a tangent to the circle \(x^{2}+y^{2}=9\), find the value of c.

Find the equation of chord of contact of tangents from the point (2, 4) to the ellipse \(2 x^{2}+5 y^{2}=20\)

Write the parametric equation of the parabola \((x+2)^{2}=-4(y+1)\)

Find the equations and lengths of major and minor axes of \(\frac{x^{2}}{9}+\frac{y^{2}}{4}=1\)

Find the equations and lengths of major and minor axes of \(4 x^{2}+3 y^{2}=12\)

Find the equations and lengths of major and minor axes of \(\frac{(x-1)^{2}}{9^{2}}+\frac{(y+1)^{2}}{16}=1\) 

Find the equations of directrices, latus rectum and length of latus rectums of the following ellipse \(\frac{x^{2}}{16}+\frac{y^{2}}{9}=1\)