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A parabola V whose focus is s(0,0) and passing through P (3,4). Equation of tangent at P to parabola is 3x 4y-25=0. A chord through S parallel to tangent at P intersects the parabola at A and B. Which of the following are correct? 1. Length of AB is 20 units. 2. Latus rectum of parabola is 20 units 3. Only one real normal can be drawn from the point (-3,-4) 4. Only one real normal can be drawn from the point (-6,-8)?
Most Upvoted Answer
A parabola V whose focus is s(0,0) and passing through P (3,4). Equati...
Given Information:
- Focus of parabola V is s(0,0).
- Parabola V passes through point P(3,4).
- Equation of tangent at P to parabola V is 3x + 4y - 25 = 0.
- A chord through S parallel to tangent at P intersects the parabola at A and B.
To Find:
Which of the following statements are correct?
- Length of AB is 20 units.
- Latus rectum of parabola is 20 units.
- Only one real normal can be drawn from the point (-3,-4).
- Only one real normal can be drawn from the point (-6,-8).
Solution:
Step 1: Find the equation of parabola V
As the focus of parabola V is s(0,0), the equation of parabola can be written as x² = 4ay.
Let P be a point on the parabola V. Hence, (3,4) lies on the parabola.
Substituting the coordinates of point P in the equation of parabola, we get:
3² = 4a(4)
a = 9/16
Therefore, the equation of parabola V is x² = (9/4)y.
Step 2: Find the coordinates of point S
As the focus of parabola V is s(0,0), the coordinates of point S are (0,1/a).
Substituting the value of a, we get S(0,16/9).
Step 3: Find the coordinates of points A and B
As chord AB is parallel to tangent at P, the slope of AB is equal to the slope of tangent at P.
Slope of tangent at P is (-3/4).
Let the coordinates of point A be (h, k). As point A lies on the parabola V, we have h² = (9/4)k.
As chord AB is parallel to tangent at P, the coordinates of point B can be written as (h + 4k/3, k + 3h/4).
As chord AB passes through point S, the coordinates of point B can be written as (4k/3, k + 3h/4).
As chord AB is a part of parabola V, the coordinates of point B can be written as [(9/4)k + 4k/3, k + 3(9/4)k/4].
Solving the above equations, we get h = 3, k = 27/4.
Therefore, the coordinates of points A and B are A(3, 27/4) and B(4, 9).
Step 4: Check the given statements
- Length of AB is 20 units.
Using distance formula, we find
Community Answer
A parabola V whose focus is s(0,0) and passing through P (3,4). Equati...
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A parabola V whose focus is s(0,0) and passing through P (3,4). Equation of tangent at P to parabola is 3x 4y-25=0. A chord through S parallel to tangent at P intersects the parabola at A and B. Which of the following are correct? 1. Length of AB is 20 units. 2. Latus rectum of parabola is 20 units 3. Only one real normal can be drawn from the point (-3,-4) 4. Only one real normal can be drawn from the point (-6,-8)?
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A parabola V whose focus is s(0,0) and passing through P (3,4). Equation of tangent at P to parabola is 3x 4y-25=0. A chord through S parallel to tangent at P intersects the parabola at A and B. Which of the following are correct? 1. Length of AB is 20 units. 2. Latus rectum of parabola is 20 units 3. Only one real normal can be drawn from the point (-3,-4) 4. Only one real normal can be drawn from the point (-6,-8)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A parabola V whose focus is s(0,0) and passing through P (3,4). Equation of tangent at P to parabola is 3x 4y-25=0. A chord through S parallel to tangent at P intersects the parabola at A and B. Which of the following are correct? 1. Length of AB is 20 units. 2. Latus rectum of parabola is 20 units 3. Only one real normal can be drawn from the point (-3,-4) 4. Only one real normal can be drawn from the point (-6,-8)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parabola V whose focus is s(0,0) and passing through P (3,4). Equation of tangent at P to parabola is 3x 4y-25=0. A chord through S parallel to tangent at P intersects the parabola at A and B. Which of the following are correct? 1. Length of AB is 20 units. 2. Latus rectum of parabola is 20 units 3. Only one real normal can be drawn from the point (-3,-4) 4. Only one real normal can be drawn from the point (-6,-8)?.
A parabola V whose focus is s(0,0) and passing through P (3,4). Equation of tangent at P to parabola is 3x 4y-25=0. A chord through S parallel to tangent at P intersects the parabola at A and B. Which of the following are correct? 1. Length of AB is 20 units. 2. Latus rectum of parabola is 20 units 3. Only one real normal can be drawn from the point (-3,-4) 4. Only one real normal can be drawn from the point (-6,-8)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A parabola V whose focus is s(0,0) and passing through P (3,4). Equation of tangent at P to parabola is 3x 4y-25=0. A chord through S parallel to tangent at P intersects the parabola at A and B. Which of the following are correct? 1. Length of AB is 20 units. 2. Latus rectum of parabola is 20 units 3. Only one real normal can be drawn from the point (-3,-4) 4. Only one real normal can be drawn from the point (-6,-8)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parabola V whose focus is s(0,0) and passing through P (3,4). Equation of tangent at P to parabola is 3x 4y-25=0. A chord through S parallel to tangent at P intersects the parabola at A and B. Which of the following are correct? 1. Length of AB is 20 units. 2. Latus rectum of parabola is 20 units 3. Only one real normal can be drawn from the point (-3,-4) 4. Only one real normal can be drawn from the point (-6,-8)?.
Solutions for A parabola V whose focus is s(0,0) and passing through P (3,4). Equation of tangent at P to parabola is 3x 4y-25=0. A chord through S parallel to tangent at P intersects the parabola at A and B. Which of the following are correct? 1. Length of AB is 20 units. 2. Latus rectum of parabola is 20 units 3. Only one real normal can be drawn from the point (-3,-4) 4. Only one real normal can be drawn from the point (-6,-8)? in English & in Hindi are available as part of our courses for JEE.
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