Home
Class 12
MATHS
Let Pi and Pi ' be the feet of the perpe...

Let `P_i` and `P_i '` be the feet of the perpendiculars drawn from the foci `Sa n dS '` on a tangent `T_i` to an ellipse whose length of semi-major axis is 20. If `sum_(i=0)^(10)(S P_i)(S^(prime)P_i ')=2560 ,` then the value of eccentricity is (a)`1/5` (b) `2/5` (c) `3/5` (d) `4/5`

A

`1//5`

B

`2//5`

C

`3//5`

D

`4//5`

Text Solution

Verified by Experts

`underset(i=i)overset(10)sum(SP_(i))(S'P_(i))=2560`
or `10b^(2)=2560`
`or b^(2)=256`
or b=16
Now, `256=400(1-e^(2))`
or `1-e^(2)=(16)/(25)`
`e=(3)/(5)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If F_1 and F_2 are the feet of the perpendiculars from the foci S_1a n dS_2 of the ellipse (x^2)/(25)+(y^2)/(16)=1 on the tangent at any point P on the ellipse, then prove that S_1F_1+S_2F_2geq8.

Let d_1a n dd_2 be the length of the perpendiculars drawn from the foci Sa n dS ' of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 to the tangent at any point P on the ellipse. Then, S P : S^(prime)P= (a) d_1: d_2 (b) d_2: d_1 (c) d_1 ^2:d_2 ^2 (d) sqrt(d_1):sqrt(d_2)

P_(1) and P_(2) are the lengths of the perpendicular from the foci on the tangent of the ellipse and P_(3) and P_(4) are perpendiculars from extermities of major axis and P from the centre of the ellipse on the same tangent, then (P_(1)P_(2)-P^(2))/(P_(3)P_(4)-P^(2)) equals (where e is the eccentricity of the ellipse)

If P(t^2,2t),t in [0,2] , is an arbitrary point on the parabola y^2=4x ,Q is the foot of perpendicular from focus S on the tangent at P , then the maximum area of P Q S is (a)1 (b) 2 (c) 5/(16) (d) 5

Let I_(n)=int_(0)^(pi//2)(sinx+cosx)^(n)dx(nge2) . Then the value of n. I_(n)-2(n-1)I_(n-1) is

The sum sum_(i=0)^m ((10),(i))((20),(m-1)) , where ((p),(q))=0 if p lt q , is maximum when m is equal to (A) 5 (B) 10 (C) 15 (D) 20

Let P be a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 of eccentricity edot If A ,A ' are the vertices and S ,S are the foci of the ellipse, then find the ratio area P S S ' ' : area A P A^(prime)dot

From any point P lying in the first quadrant on the ellipse (x^2)/(25)+(y^2)/(16)=1,P N is drawn perpendicular to the major axis and produced at Q so that N Q equals to P S , where S is a focus. Then the locus of Q is (a) 5y-3x-25=0 (b) 3x+5y+25=0 (c) 3x-5y-25=0 (d) none of these

The value of (1+cospi/8)(1+cos(3pi)/8)(1+cos(5pi)/8)(1+cos(7pi)/8)i s (a)1/4 (b) 3/4 (c) 1/8 (d) 3/8

If the x-coordinate of a point P on the join of Q(22,1)a n dR(5,1,-2)i s4, then find its z- coordinate.