Here, the radius of the circle,r=3 units Since, the circle touches both the axes and completely lies in the third quadrant, its centre is at(-3,-3).Now, the equation of the circle is(x-h)²+(y-k)²=r²or,{x-(-3)}²+{y-(-3)}²=3²or,(x+3)²+(y+3)²...
Here, the centre of the given circle is at(4,-4). As the circle touches both the axes, its radius is 4 units. The equation of the circle is(x-h)²+(y-k)²=r²or,(x-4)²+{y-(-4)}²=4²or,(x-4)²+(y+4)²=16or,x²-8x+16+y²+8y+16=16or,x²...
Learn the general equation of a circle when the center is at origin and when it is not in origin. Circle equation can be derived using Pythagoras theorem as well. Solve questions at BYJU’S.
Example 1: Find out the radius and center of a circle from the given equation. Also, draw the graph. (x-2)2+(y-3)2=4 Solution: The given equation is, (x-2)2+(y-3)2=4. Remember: If the minus sign is preceding the (h, k), (h, k) will be positive....
For example: 1. Find the equation of this circle: The center point is not marked on this circle, but we can find it fairly easily: So from this we can tell that our center point is (2, -3) and the radius is 4. (To find the radius, simply count the number of spaces from the...
Example:Find the value of tan 45º using sin and cos values from the unit circle. Solution: We know that, tan 45° = sin 45°/cos 45° Using the unit circle chart: sin 45° = 1/√2 cos 45° = 1/√2 Therefore, tan 45° = sin 45°/cos 45° ...
Consider a circle with center-radius equation (x−1)2+(y+2)2=9. Developing the left-hand side of the equation gives x2−2x+1+y2+4y+4=9⟹x2+y2−2x+4y−4=0, which is the standard equation of the given circle. Consider now a new example. Let x2+y2+4x−6y−12...
ExampleQuestion:1 (a,b) r (i)Findtheequationofthecirclewith centre(4,-3)andradius6. (ii)Doesthepoint(3,1)lieon,inside,or outsidethecircle? (i)Thecirclehasequation: (x–4) 2 +(y–(-3)) 2 =6 2 (x–4) 2 +(y+3) 2 =36 (ii)Substituting(3,1)intotheequation: (3–4) 2...
Free printable worksheet on the equation of a circle -- includes visual aides, model problems, exploratory activities, practice problems, and an online component
For two equations ax + by + c = 0 and px + qy + r = 0, it will have no solution when a/p = b/q ≠ c/r. What is the Equation of a Circle? The equation of a circle with radius r and center (x1, y1) is (x − x1)2 + (y − y1)2 = r2....