Find the number of terms in the A.P `3,6,9,12,….,111`

Options

A. `42`
B. `37`
C. `17`
D. `13`

Answer

A

Explanation

Ellipse `16x^(2) + 25y^(2) = 400`
`rArr (x^(2))/(25) + (y^(2))/(16) =1`
Let the points on ellipse be `P(5 cos theta_(1),4 sin theta_(1))` and `Q(5 cos theta_(2), 4 sin theta_(2))`
Circle described on PQ as diameter touches x-axis (3,0)
`5((cos theta_(1)+cos theta_(2))/(2))=3` and `4 ((sin theta_(1)+sin theta_(2))/(2)) =r`
`rArr (4)/(5) tan ((theta_(1)+theta_(2))/(2)) =(r)/(3) rArr tan ((theta_(1)+theta_(2))/(2)) =(5r)/(12)`
`rArr` Slope of `PQ =- (4)/(5) cot. (theta_(1)+theta_(2))/(2) =- (48)/(25r) =-1`