The line 4 x-7 y+10=0 intersects the parabola, y2=4 x at the points A and B. The sum of the co-ordinates of the point of intersection of the tangents drawn at the points A and B is

Question

The line 4 x-7 y+10=0 intersects the parabola, y2=4 x at the points A and B. The sum of the co-ordinates of the point of intersection of the tangents drawn at the points A and B is (A) 4 (B) 5 (C) 6 (D) 7

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/d9270d72e5aeb1cf5620d2ebd2405c67-.png" /> C.O.C. of P ( x 1, y 1) w.r.t. y 2=4 ax is yy 1=2( x + x 1) ....(1) compare with 4 x-7 y+10=0 .....(2) text to get (x1, y1)=((5/2), (7/2))

Q. The line $4 x - 7 y + 10 = 0$ intersects the parabola, $y^{2} = 4 x$ at the points $A$ and $B$ . The sum of the co-ordinates of the point of intersection of the tangents drawn at the points $A$ and $B$ is

4

5

6

7

C.O.C. of $P (x_{1}, y_{1})$
w.r.t. $y^{2} = 4 a x$ is
$y y_{1} = 2 (x + x_{1})$ ....(1)
compare with
$4 x - 7 y + 10 = 0$ .....(2)
$to get (x_{1}, y_{1}) = (\frac{5}{2}, \frac{7}{2})$

Q. The line 4x−7y+10=0 intersects the parabola, y2=4x at the points A and B. The sum of the co-ordinates of the point of intersection of the tangents drawn at the points A and B is

4

5

6

7

C.O.C. of P(x1​,y1​) w.r.t. y2=4ax is yy1​=2(x+x1​) ....(1) compare with 4x−7y+10=0 .....(2) to get (x1​,y1​)=(25​,27​)

Q. The line $4 x - 7 y + 10 = 0$ intersects the parabola, $y^{2} = 4 x$ at the points $A$ and $B$ . The sum of the co-ordinates of the point of intersection of the tangents drawn at the points $A$ and $B$ is

C.O.C. of $P (x_{1}, y_{1})$
w.r.t. $y^{2} = 4 a x$ is
$y y_{1} = 2 (x + x_{1})$ ....(1)
compare with
$4 x - 7 y + 10 = 0$ .....(2)
$to get (x_{1}, y_{1}) = (\frac{5}{2}, \frac{7}{2})$