Special Forms of an Ellipse
Category : JEE Main & Advanced
(1) If the centre of the ellipse is at point \[(h,k)\] and the directions of the axes are parallel to the coordinate axes, then its equation is \[\frac{{{(x-h)}^{2}}}{{{a}^{2}}}+\frac{{{(y-k)}^{2}}}{{{b}^{2}}}=1\].
(2) If the equation of the curve is \[\frac{{{(lx+my+n)}^{2}}}{{{a}^{2}}}\] \[+\frac{{{(mx-ly+p)}^{2}}}{{{b}^{2}}}=1\], where \[lx+my+n=0\] and \[mx-ly+p=0\] are perpendicular lines, then we substitute \[\frac{lx+my+n}{\sqrt{{{l}^{2}}+{{m}^{2}}}}=X,\] \[\frac{mx-ly+p}{\sqrt{{{l}^{2}}+{{m}^{2}}}}=Y\], to put the equation in the standard form.
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