The ratio of kinetic energy of a planet at perigee and apogee during its motion around yhe sun in elliptical orbit of eccentricity is what?

You have forgotten to provide the value for eccentricity. But no worries, we can consider eccentricity to be a general term represented by e. Apogee is the point in the elliptical orbit where the planet is farthest from the sun and perigee is the point where the planet is nearest to sun.In order to calculate the ratio of kinetic energy, we can use conservation of angular momentum.
Now, we know that angular momentum is conserved for the planet throughout the orbit. Hence,
Angular momentum at apogee = angular momentum at perigee
Let r_a be the distance at apogee and r_p be the distance at perigee. The value of r₁ and r₂ can be represented in terms of the semi major axis and eccentricity (e) as mentioned below. If a is the length of semi major axis, then
r_a= a(1+e)
and,
r_p= a(1-e)
Now, by conservation of angular momentum, if the mass of the planet is m and the velocity at apogee and perigee be v_a and v_p respectively.
m v_a r_a = m v_p r_p, or
v_a/v_p = r_p/r_a = (1-e)/(1+e)
The ratio of kinetic energy is given by  = (1/2mv_p²⁾/(1/2mv_a²) = (v_p/v_a)² =[(1+e)/(1-e)]²