Question

Find the equation of the line (in standard form Ax + By= C , please) passing through the vertex of the parabola x^2 + y- 2x + 6=0 and perpendicular to the line with equation 3x - 2y = 2 .

Answer 1

Given parabola is, x² + y - 2x + 6 = 0

i.e. y = -x² + 2x - 6

i.e. y = -x² + 2x - 1 - 5

i.e. y = -(x² - 2x + 1) - 5

i.e. y = -(x - 1)² - 5

Now by Comparing with y = a(x - h)² + k, we get,

Vertex = (h, k) = (1, -5)

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Now equation of a line that is perpendicular to the line 3x - 2y = 2 is of the form, 2x + 3y = c

Now this line passes through the point (1, -5) i.e. the vertex of the given parabola. So we have,

2*(1) + 3*(-5) = c

i.e. 2 - 15 = c

i.e. c = -13

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So the required equation of the line is, 2x + 3y = -13