Ellipse 2 Question 18

18. Find the equation of the common tangent in 1st quadrant to the circle x2+y2=16 and the ellipse x225+y24=1. Also, find the length of the intercept of the tangent between the coordinate axes.

(2005, 4M)

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Answer:

Correct Answer: 18. (a)

Solution:

  1. Let the common tangent to x2+y2=16 and x225+y24=1 be

y=mx+41+m2 and y=mx+25m2+4

Since, Eqs. (i) and (ii) are same tangent.

41+m2=25m2+416(1+m2)=25m2+49m2=12m=±2/3

Since, tangent is in Ist quadrant.

m<0m=2/3

So, the equation of the common tangent is

y=2x3+473

which meets coordinate axes at A(27,0) and 0,473.

AB=(270)2+04732=28+113=1963=143×33=1433



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