The equation of the ellipse with its centre at (1$$,$$2), focus at (6$$,$$2) and passing through the point (4$$, $$6) is

Question

The equation of the ellipse with its centre at (1$$,$$2), focus at (6$$,$$2) and passing through the point (4$$, $$6) is

Infinity Learn · Accepted Answer

Centre of the ellipse is $$C(1$$,$$2)$$. Also focus is at $$5(6$$,$$2)$$ Since axis is parallel to $$x-axis$$, equation of ellipse $$is(x$$−$$1)2a2+(y$$−$$2)2b2=1$$ It passes through (4$$,$$6)∴ $$9a2+16b2=1$$ Also     $$ae=5$$⇒    $$b2=a21$$−$$e2$$⇒    $$b2=a2$$−$$a2e2$$⇒    $$b2=a2$$−$$25$$∴    $$9a2+16a2$$−$$25=1$$∴    $$a2$$−$$5a2$$−$$45=0$$∴    $$a2=45$$ as if $$a2=5$$,$$b2=$$−$$20$$∴    $$b2=20$$

$The equation of the ellipse with its centre at (1,2), focus at (6,2) and passing through the point (4, 6) is$

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