Question

find the length of the chord x+2y=5 of the circle whose equation is x^2+y^2=9 ​

Answer 1

Length of the chord is 4 units.

Step-by-step explanation:

Equation of the given chord is x + 2y = 5 and equation of the circle is x² + y² = 9

We will find the points at which the given line intersects the circle.

Since x + 2y = 5

x = 5 - 2y -------(1)

Now by placing the value of x in the equation of the circle.

(5 - 2y)² + y² = 9

25 + 4y² - 20y + y² = 9

5y² - 20y + 16 = 0

y = $\frac{20\pm \sqrt{(-20)^{2}-320}}{10}$

y = $\frac{20\pm \sqrt{80} }{10}$

y = $\frac{20\pm 4\sqrt{5}}{10}$

y = $\frac{10\pm 2\sqrt{5}}{5}$ = 2.89, 1.10

From equation (1),

x = 5 - 2(2.89) = -0.78

x = 5 - 2(1.10) = 2.80

Now we know the given line intersects the circle at (-0.78, 2.89) and (2.80, 1.10)

Now the distance between these points = $\sqrt{(2.80+0.78)^{2}+(1.10-2.89)^{2}}$

= $\sqrt{12.82+3.204}$

= 4 units

Learn more about the circle and chords from https://brainly.in/question/1109661

Answer 2

Answer:

Length of the chord is 4 units.