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trapecia [35]
2 years ago
6

Find the equation of the circle with center (4,5) which passes through the y-intercept of the line 5x-2y+6=0​

Mathematics
1 answer:
Elena-2011 [213]2 years ago
3 0

Answer:

(x-4)^2 + (y-5)^2 = 20

Step-by-step explanation:

Rearrange the line equation of 5x - 2y + 6 = 0

So y = 5/2x +3

The y-intercept of the line equation is 3 as when x=0, y=3.

We know the Circle has the formula (x-4)^2 + (y-5)^2 = ?^2 from the question but with the intercept, we can find the entire equation as the y-intercept is (0,3) so we can substitute it into the equation to find the full equations so:

(0-4)^2 + (3-5)^2 = ?^2

This simplifies to:

(-4)^2 +(-2)^2 = ?^2

16 + 4 = 20 = ?^2

The answer is 20 so the equation of the circle is (x-4)^2 + (y-5)^2 = 20

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