$\"\"$

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(a)

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Vertex of parabola is $\"\"$ .

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Parabola axis is $\"\"$ .

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Latus rectum is $\"\"$ units.

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Lactus rectum is a line passes through the focus.

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$\"\"$

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Here Parabola axis is $\"\"$ , parabola open horizontally.

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The equation of parabola is $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in the above equation.

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$\"\"$

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Thus, the equation of parabola is $\"\"$ .

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Focus point of parabola is $\"\"$ .

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$\"\"$

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(b)

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Graph :

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Graph the equation of parabola $\"\"$ .

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$\"\"$

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Observe the graph :

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The distance between the points $\"\"$ and $\"\"$ of the first triangle is $\"\"$ .

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The distance between the points $\"\"$ and $\"\"$ of the second triangle is $\"\"$ .

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so, the length of adjacent sides of two right angle are same.

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The two right angle triangle have the common opposite side.

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Find length of the hypotenuse of the first and second right angle.

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The distance between the points : $\"\"$ .

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$\"\"$ and $\"\"$ is

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$\"\"$

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$\"\"$

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The length of the hypotenuse of the first right triangle is $\"\"$ .

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$\"\"$ and $\"\"$ is

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$\"\"$

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$\"\"$

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The length of hypotenuse of the second right triangle is $\"\"$ .

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The length of the hypotenuse of the first and second right angle are same.

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Thus, the triangles are isosceles triangle.

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$\"\"$

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(a) The equation of parabola is $\"\"$ .

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(b) The triangles are isosceles triangle.