Find the equation of the normal to the curve y= 2x\(^2\) - 5x + 10
FURTHER MATHEMATICS
WAEC 2021
Find the equation of the normal to the curve y= 2x\(^2\) - 5x + 10 at P(1, 7).
- A. y+x-3 =0
- B. y-x+6=0
- C. y - x - 6=0
- D. y -x+ 3 =0
Correct Answer: C. y - x - 6=0
Explanation
From y= 2x- 5x 10 ; dy/dx= 4x-5
But at (1, 7); m\(_1\) = (dy/dx)\(_{1,7}\)
= 4(1) - 5 = -1
Using m\(_1\)m\(_2\),= -1; m\(_2\) = 1.
Gradient m\(_2\), of normal at (1,7) is 1.
Using y - y\(_1\) = m(x - x\(_1\))
y - 7 = 1(x - 1) ;
y - 7 = x - 1
y - x - 6 = 0
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