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Maths-

General

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Question

From a point P, perpendicular tangents PQ and PR are drawn to ellipse $x to the power of 2 end exponent plus 4 y to the power of 2 end exponent equals 4$ Locus of circumcentre of triangle PQR is

$x^{2} + y^{2} = \frac{16}{5} {(x^{2} + 4 y^{2})}^{2}$
$x^{2} + y^{2} = \frac{5}{16} {(x^{2} + 4 y^{2})}^{2}$
$x^{2} + 4 y^{2} = \frac{16}{5} {(x^{2} + y^{2})}^{2}$
$x^{2} + 4 y^{2} = \frac{5}{16} {(x^{2} + y^{2})}^{2}$

The correct answer is: $x to the power of 2 end exponent plus y to the power of 2 end exponent equals fraction numerator 5 over denominator 16 end fraction open parentheses x to the power of 2 end exponent plus 4 y to the power of 2 end exponent close parentheses to the power of 2 end exponent$

$table row cell x to the power of 2 end exponent plus 4 y to the power of 2 end exponent equals 4 P text end text text l end text text i end text text e end text text s end text text end text text o end text text n end text text end text x to the power of 2 end exponent plus y to the power of 2 end exponent equals 5 text end text text L end text text e end text text t end text text end text P left parenthesis square root of 5 c o s q comma square root of 5 text end text text s end text text i end text text n end text text q end text text ) end text text end text text C end text text o end text text m end text text p end text text a end text text r end text text i end text text n end text text g end text text end text text c end text text h end text text o end text text r end text text d end text text end text text o end text text f end text text end text text c end text text o end text text n end text text t end text text a end text text c end text text t end text text end text end cell row cell text end text text w end text text i end text text t end text text h end text text end text text c end text text h end text text o end text text r end text text d end text text end text text w end text text i end text text t end text text h end text text end text text m end text text i end text text d end text text d end text text l end text text e end text text end text text p end text text o end text text i end text text n end text text t end text text end text fraction numerator x h over denominator h to the power of 2 end exponent plus 4 k to the power of 2 end exponent end fraction plus fraction numerator y 4 k over denominator h to the power of 2 end exponent plus 4 k to the power of 2 end exponent end fraction equals 1 end cell row cell fraction numerator x square root of 5 cos invisible function application theta over denominator 4 end fraction plus fraction numerator y square root of 5 sin invisible function application theta over denominator 1 end fraction equals 1 end cell row cell text end text text E end text text l end text text i end text text m end text text i end text text n end text text a end text text t end text text i end text text n end text text g end text text end text theta end cell row cell rightwards double arrow x to the power of 2 end exponent plus y to the power of 2 end exponent minus fraction numerator 5 over denominator 16 end fraction open parentheses x to the power of 2 end exponent plus 4 y to the power of 2 end exponent close parentheses to the power of 2 end exponent end cell end table$

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