II. 1. Find the equation of the common tangent of the following circle

1.	II. 1. Find the equation of the common tangent of the following circles at their point of contact(i) x2 + y2 + 10x – 2y + 22 = 0, x2 + y2 + 2x – 8y + 8 = 0(ii) x2 + y2 - 8y - 4 = 0, x2 + y2 – 2x – 4y = 0+
Answer» SOLUTION TO DETERMINE The equation of the common tangent of the following circles at their point of contact (i) x² + y² + 10x – 2y + 22 = 0 x² + y² + 2x – 8y + 8 = 0 (ii) x² + y² - 8y - 4 = 0 x² + y² – 2x – 4y = 0 EVALUATION (i) Here the given equation of the circles x² + y² + 10x – 2y + 22 = 0 x² + y² + 2x – 8y + 8 = 0 The equation of the conic passing through the circles x² + y² + 10x – 2y + 22 + k ( x² + y² + 2x – 8y + 8 ) = 0 ⇒ (1 + k) (x² + y²) + ( 10 + 2k)x - ( 2+8k)y + (22+8k) = 0 Since the above equation represents equation of a line So coefficient of x² = coefficient of y² = 0 ∴ 1 + k = 0 ⇒ k = - 1 So the required equation of tangent is OBTAINED by replacing k by - 1 Hence equation of the common tangent of the circles at their point of contact 8x + 6y + 14 = 0 ⇒ 4x + 3y + 7 = 0 (ii) Here the given equation of the circles x² + y² - 8y - 4 = 0 x² + y² – 2x – 4y = 0 Hence equation of the common tangent of the circles at their point of contact - 6x + 4y - 4 = 0 ⇒ 3x - 2y + 2 = 0 ━━━━━━━━━━━━━━━━ Learn more from Brainly :- $1.$ Find the SLOPE of the chord of parabola y^2=4x whose midpoint is (1,1). Help with explanation brainly.in/question/13409021 2. The length of the latus rectum of the parabola 13[(x-3)^2+(y-4)^2 )= (2x-3y+ 5)^2 is brainly.in/question/24980361 3. A hyperbola has its center at (3, 4), a VERTEX at the point (9, 4), and the length of its latus rectum is 3 units. An ex... brainly.in/question/30210645

II. 1. Find the equation of the common tangent of the following circles at their point of contact(i) x2 + y2 + 10x – 2y + 22 = 0, x2 + y2 + 2x – 8y + 8 = 0(ii) x2 + y2 - 8y - 4 = 0, x2 + y2 – 2x – 4y = 0+

Answer»

SOLUTION

TO DETERMINE

The equation of the common tangent of the following circles at their point of contact

(i) x² + y² + 10x – 2y + 22 = 0

x² + y² + 2x – 8y + 8 = 0

(ii) x² + y² - 8y - 4 = 0

x² + y² – 2x – 4y = 0

EVALUATION

(i) Here the given equation of the circles

x² + y² + 10x – 2y + 22 = 0

x² + y² + 2x – 8y + 8 = 0

The equation of the conic passing through the circles

x² + y² + 10x – 2y + 22 + k ( x² + y² + 2x – 8y + 8 ) = 0

⇒ (1 + k) (x² + y²) + ( 10 + 2k)x - ( 2+8k)y + (22+8k) = 0

Since the above equation represents equation of a line

So coefficient of x² = coefficient of y² = 0

∴ 1 + k = 0

⇒ k = - 1

So the required equation of tangent is OBTAINED by replacing k by - 1

Hence equation of the common tangent of the circles at their point of contact

8x + 6y + 14 = 0

⇒ 4x + 3y + 7 = 0

(ii) Here the given equation of the circles

x² + y² - 8y - 4 = 0

x² + y² – 2x – 4y = 0

Hence equation of the common tangent of the circles at their point of contact

- 6x + 4y - 4 = 0

⇒ 3x - 2y + 2 = 0

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Learn more from Brainly :-

$1.$ Find the SLOPE of the chord of parabola y^2=4x whose midpoint is (1,1). Help with explanation

brainly.in/question/13409021

2. The length of the latus rectum of the parabola

13[(x-3)^2+(y-4)^2 )= (2x-3y+ 5)^2 is

brainly.in/question/24980361

3. A hyperbola has its center at (3, 4), a VERTEX at the point (9, 4), and the length of its latus rectum is 3 units. An ex...

brainly.in/question/30210645