## Parabola

Published in: AIEEE | IIT JEE Mains | Mathematics
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• ### Dipu T

• Guwahati
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Pictorial depiction of different conic sections, different forms of parabola and details about tangent to a parabola in tabular form for comprehensive learning.

• 1
• Cross sectional view of Conic Sections : circle ellipse parabola hyperbola
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• Parabola with axis along x-axis : Direetrix -....................* Focal distance z Vertex F Q Focal chard x=a ordinate Foc x Latus rectum (g—2Q)
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• Parabola with axis along y— axis . dire trix (XI,YI) focus p axis of parabola vertex (X2,Y2) x
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Equation of parabolas Equations of tangent of all other parabolas in slope form =4ax 2' 2' 2 = 4ay Point of contact in terms of slope (m) a a 2a 2a y 2 = —4ar 2 = —4ay (2am,am2) (—2am,-a11i2) Equation of tangent in terms of slope (m) a 11 i a 2 y = —con 2 y + con Condition of Tangency a m a m 2 c = -am 2 c = con
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Equations of normal, point of contact, and condition of normality in terms of slope Y2 = 4at Equations of parabola Point of contact in terms of slope (DI) (am am) (—am2,2am) 2a m 2a Equations of normal in terms of slope (DI) 3 y = mx —2am am 3 y = mx +2am + am a = 7111 + 2a + — 2 m a y =mx —2a— 2 x = —4ay a 2 a 2 Condition of normality 3 c = —2am am 3 c = 2am + am a C 2 a m

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