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tangents and normals find the equation of the tangent line to the curve y=x^2 – 2x + 7 which is perpendicular to the line 5y – 15x =13

tangents and normals
find the equation of the tangent line to the curve y=x^2 – 2x + 7 which is perpendicular to the line 5y – 15x =13

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

y = x^2 - 2x + 7
Slope of tangent: y’ = -1/3
y' = 2x - 2
2x - 2 = \frac{-1}{3}
x = \frac{5}{6}
y = (\frac{5}{6})^2 - 2(\frac{5}{6}) + 7
y = \frac{25}{36} - \frac{60}{36} + 7
y = - \frac{35}{36} + 7 = \frac{217}{36}
Equation:
(y - \frac{217}{36}) = \frac{-1}{3}(x-\frac{5}{6})

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