The equation of tangent line to $y = 2x^2+7$, which is parallel to the line $4x-y+3 = 0$ is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $4x-y+5=0$
Given curve: $y = 2x^2 + 7$
Given line: $4x - y + 3 = 0 \Rightarrow y = 4x + 3$
Slope of given line: $m = 4$
Slope of tangent to curve: $\frac{dy}{dx} = 4x$
Set equal to 4: $4x = 4 \Rightarrow x = 1$
Corresponding $y$ on curve: $y = 2(1)^2 + 7 = 9$
Equation of tangent: $y - 9 = 4(x - 1) \Rightarrow y = 4x + 5$
=> 4x − y + 5 = 0