Circles MCQ Quiz in தமிழ் - Objective Question with Answer for Circles - இலவச PDF ஐப் பதிவிறக்கவும்

The original circle has the equation . Shifting the circle 3 units to the right affects only the x-coordinate of the center. The new center becomes (6, -4). The radius remains unchanged at 5. Therefore, the new equation of the circle is . 

The standard equation for this circle is . Rewriting in the form , we have . Thus, . The correct answer is -100.

The standard form of the circle's equation is . Expanding gives . Simplifying yields . Subtracting 25 from both sides results in . Thus, . The correct answer is -20.

To find the value of , we first write the equation of the circle in standard form . Expanding, we get . The given equation is , which can be compared to . Setting the constant terms equal, we find that . Therefore, the correct answer is -13.

A full revolution is radians. In 2 minutes, the wheel rotates through radians. In 30 seconds (which is of 2 minutes), it rotates through radians. Option 1 is correct. Option 2 (), Option 3 (), and Option 4 () do not represent the correct number of radians for 30 seconds.

To determine the circumference, we use . Given that the arc length is inches and the arc measure is , let the circumference be . Thus, . Simplifying results in . Therefore, . Solving for , we multiply both sides by and , resulting in . Hence, the circumference is inches.

The standard form of the equation of a circle is where is the center and is the radius. For a circle centered at with a radius of , the equation becomes . Therefore, . Thus, the correct option is .

To find the center, we need to complete the square. The given equation is . First, rewrite the equation grouping and terms: . Complete the square for : . Complete the square for : . Substituting back, we get , simplifying to . The center is .

Using the relationship , where the arc length is inches and the arc measure is , let denote the circumference. So, . Simplifying results in . Then, . Solving for , we cross-multiply to get , which gives . Thus, the circumference is inches.

To find the equation of the circle, we first determine the radius. The radius is the distance between the center and the point . Using the distance formula, . Thus, the radius is . The equation of the circle is . Substituting , , and , we get .