Question

Outdoor games like kite flying give us immense pleasure and happiness. Balancing a kite is important to fly it. The length of each portion (left and right) of the horizontal support must be of the bottom portion of the vertical support. Also, the length of the top portion of the 3 1 vertical support must be of the bottom portion. 3

Based on the given information, answer the following questions. (a) What is the total length of the vertical and horizontal supports in terms of x.

(1) (b) Find the value of x, if the sum of the lengths of the vertical support and horizontal support is 16 cm.

(1)

(c) A y cm long stick is required to make the sides and both the supports of the kite. If y satisfies the equation y + 16 = 2y - 16, then find the value of y.​

Answer 1

Answer:

Radius, r = 4, and center (h, k) = (-2, 3).

We know that the equation of a circle with centre (h, k) and radius r is given as

→ (x – h)² + (y – k)² = r² \: \: \: ….(1)→(x–h)²+(y–k)²=r²….(1)

Now, substitute the radius and center values in (1), we get

Therefore, the equation of the circle is

→ (x + 2)²+ (y – 3)² = (4)²→(x+2)²+(y–3)²=(4)²

→ x²+ 4x + 4 + y² – 6y + 9 = 16→x²+4x+4+y²–6y+9=16

Now, simplify the above equation, we get:

→ x² + y²+ 4x – 6y – 3 = 0→x²+y²+4x–6y–3=0

Thus, the equation of a circle with center (-2, 3) and radius 4 is :

→ x² + y²+ 4x – 6y – 3 = 0→x²+y²+4x–6y–3=0