Question

(at2, 2at) is a point on the line 2x - 5y + 12a = 0; from this
find the coordinates of two points on the line.
​

Answer 1

SOLUTION

GIVEN

(at², 2at) is a point on the line 2x - 5y + 12a = 0

TO DETERMINE

The coordinates of two points on the line

EVALUATION

Here it is given that

(at², 2at) is a point on the line 2x - 5y + 12a = 0

So by the given condition

$\sf{2a {t}^{2} - 10at + 12a = 0 }$

$\sf{ \implies \: {t}^{2} - 5t + 6 = 0 }$

$\sf{ \implies \: {t}^{2} - 3t - 2t + 6 = 0 }$

$\sf{ \implies \: (t - 3)(t - 2) = 0 }$

$\sf{ \implies \: t = 3 \:, \: 2 }$

For t = 3 the point is (9a,6a)

For t = 2 the point is (4a,4a)

FINAL ANSWER

Hence the required two points are

(9a,6a) and (4a,4a)

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