From the point P(3, 4) tangents PA and PB are drawn to the circle `x^(2)+y^(2)+4x+6y-12=0`. The area of `Delta` PAB in square units, is

Options

A. `(1323)/(42)`
B. `(1715)/(74)`
C. `(926)/(17)`
D. `(1409)/(13)`

Answer

B

Explanation

Clearly , AB is the chord of contact of tangents drawn from P(3, 4) to the circle `x^(2)+y^(2)+4x+6y-12=0`.
Therefore, equation of AB is
`3x+4y+2(x+3)+3(y+4)-12=0`
`rArr 5x+7y+6=0`

In `DeltaPAC`, we have
`tan theta = (CA)/(PA) rArr tan theta=(5)/(sqrt(9+16+12+24-12))=(5)/(7)`
`:. sin 2 theta = (2 tan theta)/(1+tan^(2)theta)rArr sin 2 theta=(70)/(74)`
`:. "Area of " DeltaPAB=(1)/(2)xxPAxxPBxxsin20`
`rArr "Area of " DeltaPAB = (1)/(2)xx7xx7xx(70)/(74) "sq. units"=(1715)/(74)`sq. units.