The length of the tangent from (-4, 6) to 2x² + 2y2 = 3 is:
Answers
Step-by-step explanation:
This is how to calculate it:
Identify the centre of the circle. It is (0, 0).
Work out by Pythagoras the distance from the centre of the circle to the given point.
c² = a² + b² = (-4–0)² + (6–0)² = 16 + 36 = 52
So c = √52
Work out the radius of the circle. 2x² + 2y² = 3 so x² + y² = 1.5 so the radius = √1.5
Realise that the length we are trying to find is one side of a right-angled triangle, and we have just calculated the other two sides. So, again, use Pythagoras:
a² + b² = c²
a² + (√1.5)² = (√52)²
So a² + 1.5 = 52
So a² = 50.5
So a = √50.5, which is roughly 7.11.
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