SATHEE: Parabola 3 Question 5

Parabola 3 Question 5

5. A solution curve of the differential equation $(x^{2} + x y + 4 x + 2 y + 4) \frac{d y}{d x} - y^{2} = 0, x > 0,$ passes through the point $(1, 3)$ . Then, the solution curve

(a) intersects $y = x + 2$ exactly at one point

(2016 Adv.)

(b) intersects $y = x + 2$ exactly at two points

(d) does not intersect $y = (x + 3)^{2}$

Show Answer

Answer:

Correct Answer: 5. (a, d)

Solution:

Since, $R - a, a t - \frac{1}{t}$ lies on $y = 2 x + a$ .

$\Rightarrow a \cdot t - \frac{1}{t} = - 2 a + a \Rightarrow t - \frac{1}{t} = - 1$

Thus, length of focal chord

$= a t + {\frac{1}{t}}^{2} = a t - {\frac{1}{t}}^{2} + 4 = 5 a$

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Parabola 3 Question 5

5. A solution curve of the differential equation (x2+xy+4x+2y+4)dydx−y2=0,x>0, passes through the point (1,3). Then, the solution curve

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5. A solution curve of the differential equation $(x^{2} + x y + 4 x + 2 y + 4) \frac{d y}{d x} - y^{2} = 0, x > 0,$ passes through the point $(1, 3)$ . Then, the solution curve