Question:
The equation of the tangent to the curve given by \( x^2 + 2x - 3y + 3 = 0 \) at the point \( (1,2) \) is
The equation of the tangent to the curve given by \( x^2 + 2x - 3y + 3 = 0 \) at the point \( (1,2) \) is
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Use implicit differentiation when equation is not explicitly solved for \(y\).
Updated On: Apr 30, 2026
- \( 4x - 3y - 2 = 0 \)
- \( 3y - 4x - 2 = 0 \)
- \( 4x + 3y + 2 = 0 \)
- \( 4x + 3y - 2 = 0 \)
- \( 4y - 3x + 2 = 0 \)
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The Correct Option is B
Solution and Explanation
Concept:
Slope of tangent is given by:
\[
\frac{dy}{dx}
\]
Step 1: Differentiate implicitly. \[ 2x + 2 - 3\frac{dy}{dx} = 0 \] \[ \frac{dy}{dx} = \frac{2x+2}{3} \]
Step 2: Find slope at \( (1,2) \). \[ m = \frac{2(1)+2}{3} = \frac{4}{3} \]
Step 3: Equation of tangent. \[ y - 2 = \frac{4}{3}(x - 1) \] \[ 3y - 6 = 4x - 4 \Rightarrow 3y - 4x - 2 = 0 \]
Step 1: Differentiate implicitly. \[ 2x + 2 - 3\frac{dy}{dx} = 0 \] \[ \frac{dy}{dx} = \frac{2x+2}{3} \]
Step 2: Find slope at \( (1,2) \). \[ m = \frac{2(1)+2}{3} = \frac{4}{3} \]
Step 3: Equation of tangent. \[ y - 2 = \frac{4}{3}(x - 1) \] \[ 3y - 6 = 4x - 4 \Rightarrow 3y - 4x - 2 = 0 \]
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