find the equation of the ellipse with major axis along the x-axis and passing through the point (4, 3) and (-1, 4)
Answers
Answer:
247
Step-by-step explanation:
Given that major axis is along x-axis Required equation of ellipse is x^ 2 a^ 2 + y^ 2 b^ 2 =1 0 Given that the point (4,3)\&(-1,4) lie on the ellipse So, the points (4, 3) and (- 1, 4) lie on the ellipse & satisfy the ellipse equation. Put y=3 in 0 (4)^ 2 a^ 2 + (3)^ r b^ 3 =1; x = 4; Rightarrow 16 a^ 2 + 9 b^ 2 =1 0 Put x=-1;y=4 is in( overline z Rightarrow (-1)^ gamma a^ gamma + (4)^ gamma b^ gamma =1; Rightarrow 1 a^ x + 16 b^ 2 =1 0 оия equations аrе 16/(a ^ 7) + 9/(b ^ 7) = 1 * 1/(a ^ 2) + 16/(b ^ 8) = 1; Rightarrow 1 a^ * =1- 16 b^ 2; Put 1 a^ gamma in( hat z ) Rightarrow 16 a^ gamma + 9 b^ gamma =1 Rightarrow16(1- 16 b^ gamma )^ + 9 b^ gamma =1; Rightarrow -256+9 b^ 7 =1-16 Rightarrow b^ 2 = 247 15; b^ gamma = 24 mp 15 in Theta 1 a^ gamma =1- 16 b^ gamma Rightarrow 1 a^ gamma = 7 247; Rightarrow a^ 2 = 247 7 •• Required equation of ellipse is Put x^ 7 7 + y^ 2 ( 247 15 ) =1 7x^ 7 247 + 15y^ 7 247 =1; Rightarrow7x^ 2 +15y^ 2 =247.
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