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JEE MainMathematicsModerateParabola
Line 2y + x =8 cuts the parabola y^2 = 4x at point A and B. Now
normal at A and B cuts at point P. Another normal from P (not passing
through A, B) is drawn. If equation of this normal is y = -4x + 25c the
value of (10+c) is
-4x + 25c gS] rc (10+c)dk eku gS&
Show answer and solution
[IMAGE] A,B, C are co-normal points lg
⇒slope of normal izo.krk m_1, m_2, m_3,
⇒ m_1+m_2+m_3 = 0....(i)
As B also lies on line pqafd B js[kk ij fLFkr gS ⇒ (am^2, -2am)
⇒ m^2 - 4m -8 = 0
⇒ m_1+ m_2 = 4.....(ii)
From (1) and (2)
m_3 =-4
Now equation of normal vc
y=m_3x - 2am_3 - am_3^3
y=-4x+8+64
y=-4x + 72
⇒slope of normal izo.krk m_1, m_2, m_3,
⇒ m_1+m_2+m_3 = 0....(i)
As B also lies on line pqafd B js[kk ij fLFkr gS ⇒ (am^2, -2am)
⇒ m^2 - 4m -8 = 0
⇒ m_1+ m_2 = 4.....(ii)
From (1) and (2)
m_3 =-4
Now equation of normal vc
y=m_3x - 2am_3 - am_3^3
y=-4x+8+64
y=-4x + 72
Source: Grass-G / M-26 Mathematics Paper 1 15 Jan.docx
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