CBSE (Science) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for Find the Points on the Curve X2 + Y2 − 2x − 3 = 0 at Which the Tangents Are Parallel to the X-axis ? - CBSE (Science) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

Find the points on the curve x2 + y2 − 2x − 3 = 0 at which the tangents are parallel to the x-axis ?

Solution

Let (x1, y1) be the required point.

\[\text { Since the point lie on the curve } . \]

\[\text { Hence } {x_1}^2 + {y_1}^2 - 2 x_1 - 3 = 0 . . . \left( 1 \right)\]

\[\text { Now }, x^2 + y^2 - 2x - 3 = 0 \]

\[ \Rightarrow 2x + 2y \frac{dy}{dx} - 2 = 0\]

\[ \therefore \frac{dy}{dx} = \frac{2 - 2x}{2y} = \frac{1 - x}{y}\]

\[\text { Now,} \]

\[\text { Slope of the tangent } = \left( \frac{dy}{dx} \right)_\left( x_1 , y_1 \right) =\frac{1 - x_1}{y_1}\]

\[\text { Slope of the tangent } = 0 (\text { Given )}\]

\[ \therefore \frac{1 - x_1}{y_1} = 0\]

\[ \Rightarrow 1 - x_1 = 0\]

\[ \Rightarrow x_1 = 1\]

\[\text { From (1), we get }\]

\[ {x_1}^2 + {y_1}^2 - 2 x_1 - 3 = 0\]

\[ \Rightarrow 1 + {y_1}^2 - 2 - 3 = 0\]

\[ \Rightarrow {y_1}^2 - 4 = 0\]

\[ \Rightarrow y_1 = \pm 2\]

\[\text { Hence, the points are }\left( 1, 2 \right)\text { and }\left( 1, - 2 \right).\]

  Is there an error in this question or solution?
Solution for question: Find the Points on the Curve X2 + Y2 − 2x − 3 = 0 at Which the Tangents Are Parallel to the X-axis ? concept: Maximum and Minimum Values of a Function in a Closed Interval. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
S
View in app×