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from the point M(1,3) a tangent is drawn at point p to the parabola 2{(x-6 )2 + (y-6)2}=(x+y-4)2. Find the measure of angleMSP where S is the focus of the parabola

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4 years ago

```							First of all the given eqn.  2{(x-6 )2 + (y-6)2}=(x+y-4)2 is not a defined parabola as it consists both x and y variables with power 2 and neither it gets cancelled out from R.H.Sso please first check the question.and mention again the suitable parsbolic eqn.only one varable either x or y should have power 2.
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4 years ago
```							Point 1,3 lie on the directrix of the given parabola and focus is 6,6  we have to find angle msp now think about normal parabola angle msp is 90° and this will hold for all parabola and the given equation represent a parabola of focus 6,6 and directrix x+y-4
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2 years ago
```							the angle msp is independent of coordinate system hence we shift the parabola2{(x-6)^2+(y-6)^2}=(x+y-4)^2 parallel to y axis the angle msp never change hence the equation of parabola becomes y^2=4axpoint p(at^2,2at)equation of tangent to the parabola y^2=4ax isty=x+at^2  ---(1)dirctrix cut axis at(-a,0)putting x in point(-a,0) in eqn(1) we get coordinates of mx=-ay=a(t^2-1)/tslope msp= (2at-0)/(at^2-a)=(2t)/(t^2-1)slope msm= -(t^2-1)/2tmsp×msm= -1hence angle is 90°
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2 years ago
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