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Grade 12Differential Calculus

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.

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 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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