Question

Case Study
A park is designed in form of a circle.at centre there is a fountain. The entry gate is shown at A
Consider coordinate of fountain (centre 0) of circle is (29 -1, 7) and coordinate of point A is (-3, -1).
(a) I radius of circle is 10 units, then possible values of a are
(1) 4,2
(ii) - 4,2
(in) 4,-2
(iv) - 4, - 2
(b) Distance AB -
(0) 10 units
(ii) 20 units
(iii) 10/2 units
(iv) 5 units
() If we consider, point A lies on x-axis, the what is the possible value of x-coordinate of A, take a = 2
(iii) -3+V51
(iv) 3
(d) If we consider, point B lies on y-axis then what is the possible value of y-coordinate of B take a = 2
(1) 7691
(11) -74791
(iv) -7
(e) AOB form an
() equilateral triangle
(11) isosceles right angled triangles
(ili) scalene triangle
(iv) collinear points​

Answer 1

Answer:

The correct answer is $a=-4, a=2$

Step-by-step explanation:

Step 1: A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced out from the centre. The radius of a circle is measured from the centre to the edge. The line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.

Step 2: A circle is a fundamental 2D form whose radius is quantified. The inner and exterior parts of the aircraft are separated by the circles. It resembles a line segment in several ways. Consider the line segment being bent till the ends meet. Make sure the loop is perfectly round by arranging it.

A two-dimensional figure with an area and perimeter is a circle. The distance around a circle, or its circumference, is also known as its perimeter. The area of a circle is the area that it surrounds on a two-dimensional plane.

Step 3: Now $\mathrm{OA}=10$ units

$\begin{aligned}& O A=\sqrt{(2 \alpha-1+3)^2+(7+1)^2} \\& 10=\sqrt{4 a^2+4+8 \alpha+64}\end{aligned}$

Squaring

$\begin{aligned}& 100=4 a^2+8 a+68 \\& 4 a^2+8 a-32=0 \\& a^2+2 a-8=0 \\& a^2+4 a+2 a-8=0 \\& a(a+4)+2(a-8)=0 \\& (a-4)(a-2)=0 \\& a=-4, a=2\end{aligned}$

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