If `f: RvecNuu{0},` where `f` (area of triangle joining points `P(5,0),Q(8,4)a n dR(x , y)` such that angle PRQ is a right angle `=` number of triangles, then which of the following is true? `f(5)=4` (b) `f(7)=0` `f(6, 25)=2` (d) `f(x)i snot`

Options

A. `f(5)=4`
B. `f(7)=0`
C. `f(6.25)=2`
D. `f(4.5)=4`

Answer

A, B, C, D

Explanation

Hence` angle PRQ=pi//2` and points P, Q, R lie on the circle with PQ as diameter.
Also, `PQ=5.`

Now, the maximum area of the triangle is
`Delta_(max)=(1)/(2)(5)((5)/(2))=6.25`
For area = 5, we have four symmetrical positions of point R (shown as `R_(1), R_(2),R_(3), R_(4)`).
For area = 6.25, we have exactly two points.
For area = 7, no such points exist.