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Conic Sections ...

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  • Question 1
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    Equation of the parabola having focus $$(3,2)$$ and Vertex $$(-1,2)$$ is 

  • Question 2
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    Directions For Questions

    Equation of a circle is  $$S={x}^{2}+{y}^{2}+2gx+2fy+c$$
    Its notation is $${S}_{1}={x}_{1}x+{y}_{1}y+g\left(x+{x}_{1}\right)+f\left({y}_{1}+y\right)+c$$
    $${S}_{11}={x}_{1}^{2}+{y}_{1}^{2}+2g{x}_{1}+2f{y}_{1}+c$$
    $$\left(i\right)$$Location of $$P\left({x}_{1},{y}_{1}\right):$$
    $$P$$ lies inside the circle $$S=0$$, if $${S}_{11}<0$$
    $$P$$ lies outside the circle $$S=0$$ if $${S}_{11}>0$$
    $$P$$ lies on the circle $$S=0,$$ if $${S}_{11}=0$$
    $$\left(ii\right)$$Tangent at $$P\left({x}_{1},{y}_{1}\right)$$ on the circle $$S=0,$$ is $${S}_{1}=0$$
    $$\left(iii\right)$$ Length of the tangent from the point $$\left({x}_{1},{y}_{1}\right)$$ to the circle $$S=0$$ is $$\sqrt{{S}_{11}}$$
    $$\left(iv\right)$$Pair of tangents $$PQ,PR$$ from $$P\left({x}_{1},{y}_{1}\right)$$ is $${S}_{1}^{2}={S}_{11}S$$
    $$\left(v\right)$$Chord of contact $$QR$$ of tangents from $$P\left({x}_{1},{y}_{1}\right)$$ is $${S}_{1}=0$$
    $$\left(vi\right)$$Chord of $$S=0$$ with midpoint $$\left({x}_{1},{y}_{1}\right)$$ is $${S}_{1}={S}_{11}$$
    Based on the above information,answer the following questions:

    ...view full instructions

    The equation of the circle whose radius is $$5$$units and which touches the circle, $${x}^{2}+{y}^{2}-2x-4y-20=0$$ at the point $$\left(5,5\right)$$ is

  • Question 3
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    If the line $$y = x \sqrt{3} - 3$$ cuts the parabola $$y^2 = x + 2$$ at $$P$$ and $$Q$$ and if $$A$$ be the points $$(\sqrt{3}, 0)$$ , then $$AP.AQ$$ is

  • Question 4
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    The equation $$\dfrac{x^2}{2-a}+\dfrac{y^2}{a-5}+1=0$$ represents an ellipse if $$a\in$$

  • Question 5
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    The equation of the latusrecta of the ellipse $$9x^{2}+4^{2}-18x-8y-23=0$$ are 

  • Question 6
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    In the $$xy$$ plane,  the segment with end points$$(3,8)$$ and $$(
    5,2)$$ is the diameter of the circle. The  point $$(k,10)$$ lies on the circle for:

  • Question 7
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    Find the equation of the circle which passes through the points $$(2,-2)$$ and $$(3,4)$$. And whose centre lies on the line $$x+y=2$$.

  • Question 8
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    The equation of the latus rectum of the parabola $${ x }^{ 2 }+4x+2y=0$$ is

  • Question 9
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    A circle of radius $$2$$ lies in the first quadrant and touches both the axes of co-ordinates. Then the equation of the circle with centre $$(6, 5)$$ and touching the above circle externally is

  • Question 10
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    The equation $$2x^2+3y^2-8x-18y+35=\lambda$$ represents?

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