Circles Test 14

Directions For Questions

Equation of a circle is $$S={x}^{2}+{y}^{2}+2gx+2fy+c$$
Its notation is $${S}_{1}={x}_{1}x+{y}_{1}y+g\left(x+{x}_{1}\right)+f\left({y}_{1}+y\right)+c$$
$${S}_{11}={x}_{1}^{2}+{y}_{1}^{2}+2g{x}_{1}+2f{y}_{1}+c$$
$$\left(i\right)$$Location of $$P\left({x}_{1},{y}_{1}\right):$$
$$P$$ lies inside the circle $$S=0$$, if $${S}_{11}<0$$
$$P$$ lies outside the circle $$S=0$$ if $${S}_{11}>0$$
$$P$$ lies on the circle $$S=0,$$ if $${S}_{11}=0$$
$$\left(ii\right)$$Tangent at $$P\left({x}_{1},{y}_{1}\right)$$ on the circle $$S=0,$$ is $${S}_{1}=0$$
$$\left(iii\right)$$ Length of the tangent from the point $$\left({x}_{1},{y}_{1}\right)$$ to the circle $$S=0$$ is $$\sqrt{{S}_{11}}$$
$$\left(iv\right)$$Pair of tangents $$PQ,PR$$ from $$P\left({x}_{1},{y}_{1}\right)$$ is $${S}_{1}^{2}={S}_{11}S$$
$$\left(v\right)$$Chord of contact $$QR$$ of tangents from $$P\left({x}_{1},{y}_{1}\right)$$ is $${S}_{1}=0$$
$$\left(vi\right)$$Chord of $$S=0$$ with midpoint $$\left({x}_{1},{y}_{1}\right)$$ is $${S}_{1}={S}_{11}$$
Based on the above information,answer the following questions:

...view full instructions

Circles Test 1...

Question 1

$${x}^{2}+{y}^{2}+18x+16y+120=0$$

$${x}^{2}+{y}^{2}-18x-16y+120=0$$

$${x}^{2}+{y}^{2}-18x-16y-120=0$$

$${x}^{2}-{y}^{2}-18x-16y-120=0$$

Question 2

no value of $$k$$

exactly one integral $$k$$

exactly one non integral $$k$$

two real values of $$k$$

Question 3

$${ x }^{ 2 }+{ y }^{ 2 }+7x+3y+16=0$$

$${ x }^{ 2 }+{ y }^{ 2 }+7x-3y-16=0$$

$${ x }^{ 2 }+{ y }^{ 2 }+4x+5y-16=0$$

$${ x }^{ 2 }+{ y }^{ 2 }+5x+8y+30=0$$

Question 4

$${x}^{2}+{y}^{2}+8x=0$$

$${x}^{2}+{y}^{2}-8x=0$$

$${x}^{2}+{y}^{2}+8y=0$$

$${x}^{2}+{y}^{2}-8y=0$$

Question 5

$$(x - 6)^2 + (y - 5)^2 = 4$$

$$(x - 6)^2 + (y - 5)^2 = 9$$

$$(x - 6)^2 + (y - 5)^2 = 36$$

none of these

Question 6

$$x^2 + y^2 - 3x - 7y + 12 = 0$$

$$x^2 + y^2 -4x - 6y + 12 = 0$$

$$x^2 + y^2 - 6x - 4y + 12 = 0$$

$$x^2 + y^2 - 5x - 5y + 12 = 0$$

Question 7

$$1$$

$$\dfrac{3}{4}$$

$$0$$

$$-\dfrac{3}{4}$$

Question 8

$$(3,4)$$ , $$25$$

$$(-3,4)$$ , $$5$$

$$(3,-4)$$ , $$5$$

$$(3,-4)$$ , $$25$$

Question 9

$$1$$

$$\dfrac {3}{4}$$

$$0$$

$$-\dfrac {3}{4}$$

Question 10

$$x^2+y^2-4x-9y-4=0$$

$$x^2+y^2+4x+9y+4=0$$

$$x^2+y^2+4x+6y+9=0$$

$$x^2+y^2-4x-6y-9=0$$

User

Question Analysis

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.