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TS EAMCET · Maths · Ellipse

If the normal drawn at one end of the latus rectum of the ellipse b2x2+a2y2=a2b2 with eccentricity 'e' passes through one end of the minor axis, then

  1. A e4+e2=2
  2. B e4-e2=1
  3. C e4+e2=1
  4. D e2+e=1
Verified Solution

Answer & Solution

Correct Answer

(C) e4+e2=1

Step-by-step Solution

Detailed explanation

b2x2+a2y2=a2b2 ⇒x2a2+y2b2=1 Equation of the normal to x2a2+y2b2=1 at x1, y1 is, a2xx1-b2yy1=a2-b2 ⇒ Normal at ae,b2a to one end of latus rectum is a2xae-b2yb2a=a2-b2 ⇒axe-ay=a2-b2 ⇒ab=a2-b2 ⇒ab=a2-a21-e2=a21-1+e2 ⇒b=ae2 ⇒ba=e2…