Check sibling questions

Ex 11.1, 15 - Does point (-2.5, 3.5) lie inside, outside or on

Ex 11.1,  15 - Chapter 11 Class 11 Conic Sections - Part 2
Ex 11.1,  15 - Chapter 11 Class 11 Conic Sections - Part 3 Ex 11.1,  15 - Chapter 11 Class 11 Conic Sections - Part 4 Ex 11.1,  15 - Chapter 11 Class 11 Conic Sections - Part 5 Ex 11.1,  15 - Chapter 11 Class 11 Conic Sections - Part 6 Ex 11.1,  15 - Chapter 11 Class 11 Conic Sections - Part 7 Ex 11.1,  15 - Chapter 11 Class 11 Conic Sections - Part 8

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Ex 10.1, 15 (Introduction) Does the point (–2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25? We know that equation of circle is (x − h)2 + (y − k)2 = r2 where (h, k) is the centre & r is the radius of circle If for any point (a, b) (a − h) 2 + (b − k) 2 = r2 Then point (a, b) lies on the circle (a − h) 2 + (b − k) 2 < r2 Then point (a, b) lie inside the circle (iii) (a − h) 2 + (b − k) 2 > r2 Then point (a, b) lie outside the circle Ex 10.1, 15 (Method 1) Does the point (–2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25? Given equation x2 + y2 = 25 (x – 0)2 + (y – 0)2 = 52 We know that equation of circle is (x – h)2 + (y – k)2 = r2 Here, h = 0, k = 0 & r = 5 Hence Centre = (h, k) = (0, 0) Radius = r = 5 Finding Distance between centre (0, 0) & point (−2.5, 3.5) We know that distance between two point (x1, y1) & (x2, y2) is d = √((𝑥2−𝑥1)2+(𝑦2−𝑦1)2) Putting values = √((0−(−2.5))^2+(0 −3.5)2) = √((2.5)2+(−3.5)2) = √((2.5)2+(3.5)2) = √(6.25+12.25) = √18.50 < √25 < 5 Thus, distance between centre (0,0) & point (-2.5, 3.5) is √18.50 which is less than 5 (radius) Hence point (-2.5, −3.5) lies inside the circle Ex 10.1, 15 (Method 2) Does the point (–2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25? We know that equation of circle is (x − h)2 + (y − k)2 = r2 where (h, k) is the centre & r is the radius of circle If for any point (a, b) (a − h) 2 + (b − k) 2 = r2 Then point (a, b) lies on the circle (a − h) 2 + (b − k) 2 < r2 Then point (a, b) lie inside the circle (a − h) 2 + (b − k) 2 > r2 Then point (a, b) lie outside the circle Given that Equation of circle is x2 + y2 = 25 We need to find that Point (−2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25 Putting x = −2.5 & y = 3.5 in x2 + y2 = (−2.5)2 + (3.5)2 = 6.25 + 12.25 = 18.50 < 25 Thus, (−2.5)2 + (3.5)2 < 25 i.e. (a − h) 2 + (b − k) 2 < r2 ∴ Point (−2.5, 3.5) lie inside the circle x2 + y2 =25

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.