# Ex 11.1, 15

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 11.1, 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) (i) (a − h) 2 + (b − k) 2 = r2 Then point (a, b) lies on the circle (ii) (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 11.1, 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−𝑥12+𝑦2−𝑦12 Putting values = 0−−2.52+0 −3.52 = 2.52+−3.52 = 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 11.1, 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) (i) (a − h) 2 + (b − k) 2 = r2 Then point (a, b) lies on the circle (ii) (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 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

Chapter 11 Class 11 Conic Sections

Serial order wise

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CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .