Falling Behind in Studies? Join Our Performance Improvement Batch. Enroll For Free
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
If lines 2x + 3y =10 and 2x-3y =10 are tangents at the extremities of a latus rectum of an ellipse whose centre is origin,then the length of the latus rectum is?
You know both the tangents...Their point of intersection is (5,0)...You can use the formula of pair of tangents from a point drwn from (x`, y`)....that is SS` - T² = 0......S= x²/a² + y²/b² - 1 = 0...S`= x`²/a² + y`²/b² - 1 = 0...T= xx`/a² + yy`/b² - 1 = 0...Here (x`,y`) is (5,0)....Multiply the given tangents and then compare the coefficients....A little simplified form which you will get is:::: x²/a² + y²/b²*(1- 25/a²) - 10x/a² + (25/a²) = 0....And product of tangents is:::: 4x² - 9y² - 40x + 100 = 0.....Now comapre the coefficients...from which you will get a²=1/4 and b²=11...which gives length of the latus ractum as ans:::: 44 units......
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -