about to only mathematics

Options

A. (0,3)
B. (0,5/2)
C. (0,0)
D. (0,6)

Answer

B, C

Explanation

Let point A be `(0,lambda)`
Slope of `AP=(lambda-2)/(0-1)=2-lambda`
AB and AC are parallel to the lines `y=x+2` and `y=7x+3`respectively.
Thus, slope of AB and AC are 1 and 7, respectively.
From the figure,
`tantheta=((2-lambda)-1)/(1+(2-lambda))=(7-(2-lambda))/(1+7(2-lambda))`
`rArr((1-lambda)/(3-lambda))=((5+lambda)/(15-7lambda))`
`rArr(lambda-1)(7lambda-15)=(5+lambda)(3-lambda)`
`rArr 8lambda^20lambda=0`
`A=(0,0) and (0,5//2)` .