Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Parabola

NTA Abhyas 2020 · Mathematics · Parabola

Let tangents PQ and PR are drawn from the point P(- 2,4) to the...

Let tangents PQandPQ andPRaredrawnfromthepointare drawn from the pointP(−2,4)P\left(- 2,4\right) to the parabola y2=4x.{y}^{2} = 4x . If SS is the focus of the parabola y2=4x{y}^{2} = 4x, then the value (in units)ofRS+SQof RS + SQ is equal to

Correct answer

22

Step-by-step solution

Let, Q=(t12,2t1) and R=(t22,2t2)Q = \left({t}_{1}^{2}, 2{t}_{1}\right) \text{ and } R = \left({t}_{2}^{2}, 2{t}_{2}\right), then P=(t1t2,t1+t2)=(−2,4)P = \left({t}_{1}{t}_{2}, {t}_{1} + {t}_{2}\right) = \left(- 2,4\right)

⇒t1t2=−2 and t1+t2=4⇒ {t}_{1}{t}_{2} = - 2 \text{ and } {t}_{1} + {t}_{2} = 4

Now, QS=1+t12,RS=1+t22QS = 1 + {t}_{1}^{2}, RS = 1 + {t}_{2}^{2}

⇒QS+RS=2+t12+t22⇒ QS + RS = 2 + {t}_{1}^{2} + {t}_{2}^{2}

=2+(t1+t2)2−2t1t2= 2 + {\left({t}_{1} + {t}_{2}\right)}^{2} - 2{t}_{1}{t}_{2}

=2+(4)2−2(−2)= 2 + {\left(4\right)}^{2} - 2\left(- 2\right)

=2+16+4=22= 2 + 16 + 4 = 22 units
Practice Parabola on Quantrex Academy →

More from Parabola

Let T be the tangent to the parabola y^2 = 16x at the point (64, 32) . Let L be the… JEE Advanced 2026Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to… JEE Main 2026Let chord PQ of length 3 13 of the parabola y^2 = 12x be such that the ordinates of… JEE Main 2026Let the point P be the vertex of the parabola y = x^2 - 6x + 12 . If a line passing… JEE Main 2026Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B(α, β)… JEE Main 2026Let A,B and C be the vertices of a variable right angled triangle inscribed in the… JEE Main 2026Consider the parabola P : y^2 = 4kx and the ellipse E : (x^2)/(a^2) + (y^2)/(b^2) = 1 .… JEE Main 2026Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the… JEE Main 2026Let A be the focus of the parabola y^ 2 =8 x . Let the line y=m x+c intersect the… JEE Main 2026Let the image of parabola x^ 2 =4 y , in the line x-y=1 be (y+a)^ 2 =b(x-c) , a, b, c ∈… JEE Main 2026An equilateral triangle OAB is inscribed in the parabola y^ 2 =4 x with the vertex O at… JEE Main 2026Let the locus of the mid-point of the chord through the origin O of the parabola y^ 2 =4… JEE Main 2026If the chord joining the points P_ 1 (x_ 1 , y_ 1 ) and P_ 2 (x_ 2 , y_ 2 ) on the… JEE Main 2026Let y^ 2 =12 x be the parabola with its vertex at O. Let P be a point on the parabola and… JEE Main 2026Let one end of a focal chord of the parabola y^ 2 =16 x be (16,16) . If P(α, β) divides… JEE Main 2026Let O be the vertex of the parabola x^ 2 =4 y and Q be any point on it. Let the locus of… JEE Main 2026 Full Parabola list Parabola JEE Maths PYQsJEE Mathematics PYQs All NTA Abhyas JEE Main PYQs