If the line `y=2x+k` tangent to the parabola `y=x^(2)+3x+5` then find 'k' is

Options

A. A. p=5, h=4, k=-3
B. B. p=-1, h=1, k=-3
C. C. p=-2, h=2, k=-4
D. D. p=2, h=3, k=-4

Explanation

4 Parabola, `y^(2)=16x`
Equation of chord, 2x+y=p (1)
Equation of chord having mid point (h,k) is `T=S_(1)`
`ky=8(x+h)=k^(2)-16h`
`orky-8x=k^(2)=8h`
comparing (1) and (2), we get
`(k)/(1)=(-8)/(2)=(k^(2)-8h)/(p)`
`rArrk=-4andk^(2)-8h=-4p`
From this, we get
16-8h=-4p
Clearly, h=3 and p=2.