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# Solution for Write the Equation on the Tangent to the Curve Y = X2 − X + 2 at the Point Where It Crosses the Y-axis ? - CBSE (Science) Class 12 - Mathematics

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#### Question

Write the equation on the tangent to the curve y = x2 − x + 2 at the point where it crosses the y-axis ?

#### Solution

When the curve crosses the y-axis, the point on the curve is of the form (0, y).
Here,

$y = x^2 - x + 2$

$\Rightarrow y = 0 - 0 + 2 = 2$

$\text { So, the point where the curve crosses they-axis is }(0, 2).$

$\text { Now,}$

$y = x^2 - x + 2$

$\Rightarrow \frac{dy}{dx} = 2x - 1$

$\text { Slope of the tangent },m= \left( \frac{dy}{dx} \right)_\left( 0, 2 \right) =2\left( 0 \right)-1=-1$

$\therefore \left( x_1 , y_1 \right) = \left( 0, 2 \right)$

$\text { and }$

$\text { Equation of tangent }$

$= y - y_1 = m\left( x - x_1 \right)$

$\Rightarrow y - 2 = - 1\left( x - 0 \right)$

$\Rightarrow y - 2 = - x$

$\Rightarrow x + y - 2 = 0$

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#### Video TutorialsVIEW ALL [3]

Solution for question: Write the Equation on the Tangent to the Curve Y = X2 − X + 2 at the Point Where It Crosses the Y-axis ? concept: Tangents and Normals. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
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