\[
{\text{. If a parabola touch three given straight lines, prove that each of the lines joining the points }} \\
{\text{of contact passes through a fixed point}}{\text{.}} \\
\]
Answer
369.6k+ views
\[
{\text{If two of the tangents are the axis then equation of parabola is}} \\
\sqrt {\dfrac{x}{a}} + \sqrt {\dfrac{y}{b} = 1} \\
{\text{If the third tangent is }}\dfrac{x}{f} + \dfrac{y}{g} = 1 \\
{\text{Then, the condition for the tangency is}} \\
\dfrac{f}{a} + \dfrac{g}{b} = 1 \\
{\text{So, the line }}\dfrac{x}{a} + \dfrac{y}{b} = 1{\text{ always passes through }}(f,g) \\
{\text{Note: In this type of question always start with two static straight lines}} \\
{\text{ then introduce third line with condition}}{\text{.}} \\
\]
{\text{If two of the tangents are the axis then equation of parabola is}} \\
\sqrt {\dfrac{x}{a}} + \sqrt {\dfrac{y}{b} = 1} \\
{\text{If the third tangent is }}\dfrac{x}{f} + \dfrac{y}{g} = 1 \\
{\text{Then, the condition for the tangency is}} \\
\dfrac{f}{a} + \dfrac{g}{b} = 1 \\
{\text{So, the line }}\dfrac{x}{a} + \dfrac{y}{b} = 1{\text{ always passes through }}(f,g) \\
{\text{Note: In this type of question always start with two static straight lines}} \\
{\text{ then introduce third line with condition}}{\text{.}} \\
\]
Last updated date: 30th Sep 2023
•
Total views: 369.6k
•
Views today: 8.69k
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

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

The poet says Beauty is heard in Can you hear beauty class 6 english 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

What is the past tense of read class 10 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
