SATHEE: Circle 1 Question 24

Circle 1 Question 24

24. Let $E_{1} E_{2}$ and $F_{1} F_{2}$ be the chords of $S$ passing through the point $P_{0} (1, 1)$ and parallel to the $X$ -axis and the $Y$ -axis, respectively. Let $G_{1} G_{2}$ be the chord of $S$ passing through $P_{0}$ and having slope -1 . Let the tangents to $S$ at $E_{1}$ and $E_{2}$ meet at $E_{3}$ , then tangents to $S$ at $F_{1}$ and $F_{2}$ meet at $F_{3}$ , and the tangents to $S$ at $G_{1}$ and $G_{2}$ meet at $G_{3}$ . Then, the points $E_{3}, F_{3}$ and $G_{3}$ lie on the curve

(a) $x + y = 4$

(b) $(x - 4)^{2} + (y - 4)^{2} = 16$

(d) $x y = 4$

Show Answer

Solution:

Equation of tangent at $E_{1} (- \sqrt{3}, 1)$ is

$\begin{aligned} - \sqrt{3} x + y & = 4 and at E_{2} (\sqrt{3}, 1) is \\ \sqrt{3} x + y & = 4 \end{aligned}$

Intersection point of tangent at $E_{1}$ and $E_{2}$ is $(0, 4)$ .

$∴$ Coordinates of $E_{3}$ is $(0, 4)$

Similarly, equation of tangent at $F_{1} (1, - \sqrt{3})$ and $F_{2} (1, \sqrt{3})$ are $x - \sqrt{3} y = 4$ and $x + \sqrt{3} y = 4$ , respectively and intersection point is $(4, 0)$ , i.e., $F_{3} (4, 0)$ and equation of tangent at $G_{1} (0, 2)$ and $G_{2} (2, 0)$ are $2 y = 4$ and $2 x = 4$ , respectively and intersection point is $(2, 2)$ i.e., $G_{3} (2, 2)$ . Point $E_{3} (0, 4), F_{3} (4, 0)$ and $G_{3} (2, 2)$ satisfies the line $x + y = 4$ .

Circle 1 Question 24

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Circle 1 Question 24

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu