The equation of the tangent to the curve x^2+ | vedclass

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(A) The given curve is $x^2 + y - 7 = 4x$. To find the equation of the tangent at $(x_1, y_1) = (1, 10)$,we use the transformation rules: $x^2 	o x x

Vedclass · Accepted Answer

$y = 2x + 8$

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(A) The given curve is $x^2 + y - 7 = 4x$. To find the equation of the tangent at $(x_1, y_1) = (1, 10)$,we use the transformation rules: $x^2 	o x x_1$ and $y 	o \frac{y + y_1}{2}$ and $x 	o \frac{x + x_1}{2}$. Substituting these into the equation: $x(1) + \frac{y + 10}{2} - 7 = 4 \left( \frac{x + 1}{2} ight)$ $x + \frac{y + 10}{2} - 7 = 2(x + 1)$ Multiply the entire equation by $2$: $2x + y + 10 - 14 = 4x + 4$ $2x + y - 4 = 4x + 4$ $y = 4x - 2x + 4 + 4$ $y = 2x + 8$

The equation of the tangent to the curve $x^2+y-7=4x$ at the point $(1,10)$ is

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