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A tangent to the ellipse `x^2 / a^2 + y^2 / b^2 = 1` touches at the point P on it in the first quadrant & meets the coordinate axes in A & B respectively. If P divides AB in the ratio `3: 1` reckoning from the x-axis find the equation of the tangent. |
| Answer» equation of tangent at any point on eclipse`(x cos theta)/a+(ysin theta)/b=1`co-ordinates of A`(a/costheta,0)`co-ordinates of B`(0,b/sin theta)`P is between A and B with ratio 3:1So, P`(a/(4cos theta), (3b)/(4sintheta))`=P`(a cos theta, b sin theta)``a/(4cos theta)=acostheta``cos^2theta =1/4``costheta=-1/2``sin theta=sqrt3/2`equation of tangent will be`x/(2a)+(xysqrt3)/(2b)=1``bx+aysqrt3=2ab` | |