If the equation is x^2/a^2 + y^2/b^2 = 1 then clearly a=10 (make y=0 in the equation). Because the sum of the distances to the foci is the same for any point and is 2+18=20 for (-10,0) then, as (0,b) satisfies the equation we must have
2 sqrt(b^2 + 8^2) = 20 and therefore
b= sqrt (10^2- 8^2) = sqrt (36) = 6. The equation is therefore
The vertices are vertically aligned, so the ellipse is vertical. the final equation of a vertical ellipse is (y?ok)²/a² + (x?h)²/b² = a million with center (h, ok) a ? b > 0 vertices (h, ok±a) co-vertices (h±b, ok) foci (h, ok±c), the place c² = a² ? b² prepare your documents. the middle of the ellipse is precisely midway between foci, at (0, 0). h = ok = 0 The vertices are (0, 0±10). a = 10 a² = a hundred The foci are (0, 0±2). c = 2 c² = 4 b² = a² - c² = ninety six The equation will become y²/a hundred + x²/ninety six = a million
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If the equation is x^2/a^2 + y^2/b^2 = 1 then clearly a=10 (make y=0 in the equation). Because the sum of the distances to the foci is the same for any point and is 2+18=20 for (-10,0) then, as (0,b) satisfies the equation we must have
2 sqrt(b^2 + 8^2) = 20 and therefore
b= sqrt (10^2- 8^2) = sqrt (36) = 6. The equation is therefore
x^2/100 + y^2/36 =1
The vertices are vertically aligned, so the ellipse is vertical. the final equation of a vertical ellipse is (y?ok)²/a² + (x?h)²/b² = a million with center (h, ok) a ? b > 0 vertices (h, ok±a) co-vertices (h±b, ok) foci (h, ok±c), the place c² = a² ? b² prepare your documents. the middle of the ellipse is precisely midway between foci, at (0, 0). h = ok = 0 The vertices are (0, 0±10). a = 10 a² = a hundred The foci are (0, 0±2). c = 2 c² = 4 b² = a² - c² = ninety six The equation will become y²/a hundred + x²/ninety six = a million