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TANGENTS AND NORMALS find the points on the curve x^2 + y^2 = 13 the tangent at each one of which is parallel to the line 2x + 3y = 7.

TANGENTS AND NORMALS
find the points on the curve x^2 + y^2 = 13 the tangent at each one of which is parallel to the line 2x + 3y = 7.

Grade:12

1 Answers

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

Slope of tangent = m
m = \frac{-2}{3}
x^2 + y^2 = 13
2x + 2yy' = 0
y' = \frac{-2}{3}
x = \frac{2y}{3}…..(1)
Put in curve
(\frac{2y}{3})^2 + y^2 = 13
\frac{13y^2}{9} = 13
y^2 = 9
y = \pm 3
Put in (1)
x = \pm 2

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