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Question
Answer the following:
Find the equation of the tangent to the parabola y2 = 8x which is parallel to the line 2x + 2y + 5 = 0. Find its point of contact
Solution
The equation of the tangent to the parabola y2 = 4ax in terms of slope m is y = `"mx" + "a"/"m"` and the point of contact is `("a"/"m"^2, (2"a")/"m")`.
The equation of parabola is y2 = 8x
Comparing this with y2 = 4ax, we get,
∴ 4a = 8
∴ a = 2
Slope of 2x + 2y + 5 = 0 is `-2/2` = – 1
The required tangent is parallel to it
∴ its slope = m = – 1
∴ the required equation of the tangent is
y = `(-1)"x" + 2/((-1))` = – x – 2
∴ x + y + 2 = 0
The point of contact = `("a"/"m"^2, (2"a")/"m")`
= (2, – 4)
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