If two tangents drawn from a point P to the parabola ${y^2} = 4x$ are at right angles, then the locus of P is
A. $x = 1$
B. $2x + 1 = 0$
C. $x = - 1$
D. $2x - 1 = 0$
Answer
361.2k+ views
Hint: Use the information that the locus of point p from which two perpendicular tangents are drawn to the parabola is the directrix of the parabola. So, essentially, we need to find the directrix of the given parabola.
Complete step-by-step answer:
We have given the equation of parabola as ${y^2} = 4x$. Let’s consider it as an equation ……..(1).
We know that the locus of point p from which two perpendicular tangents are drawn to the parabola is the directrix of the parabola.
Also, the standard equation to the parabola is ${y^2} = 4ax$ and when we shift the origin to the point $(h,k)$ then this equation will become ${(y - k)^2} = 4p(x - h)$. It has focus $(h + p,k)$ and the directrix is $x = h - p$.
From equation (1), we get, $h = 0,k = 0,p = 1$. So, the directrix of equation (1) is $x = 0 - 1 = - 1$. Hence, required locus is $x = - 1$.
Note: Locus, as the word says, is the path of a point under given conditions. Here we observed that the path of the point will be the directrix of the given parabola then we solved the problem.
Complete step-by-step answer:
We have given the equation of parabola as ${y^2} = 4x$. Let’s consider it as an equation ……..(1).
We know that the locus of point p from which two perpendicular tangents are drawn to the parabola is the directrix of the parabola.
Also, the standard equation to the parabola is ${y^2} = 4ax$ and when we shift the origin to the point $(h,k)$ then this equation will become ${(y - k)^2} = 4p(x - h)$. It has focus $(h + p,k)$ and the directrix is $x = h - p$.
From equation (1), we get, $h = 0,k = 0,p = 1$. So, the directrix of equation (1) is $x = 0 - 1 = - 1$. Hence, required locus is $x = - 1$.
Note: Locus, as the word says, is the path of a point under given conditions. Here we observed that the path of the point will be the directrix of the given parabola then we solved the problem.
Last updated date: 25th Sep 2023
•
Total views: 361.2k
•
Views today: 7.61k
Recently Updated Pages
What is the Full Form of DNA and RNA

What are the Difference Between Acute and Chronic Disease

Difference Between Communicable and Non-Communicable

What is Nutrition Explain Diff Type of Nutrition ?

What is the Function of Digestive Enzymes

What is the Full Form of 1.DPT 2.DDT 3.BCG

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Drive an expression for the electric field due to an class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

What is the past tense of read class 10 english CBSE
